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cake numbers
Numbers which count the maximal number of pieces in which a cake can be divided into by n planar cuts. more

The first 600 cake numbers :
1, 2, 4, 8, 15, 26, 42, 64, 93, 130, 176, 232, 299, 378, 470, 576, 697, 834, 988, 1160, 1351, 1562, 1794, 2048, 2325, 2626, 2952, 3304, 3683, 4090, 4526, 4992, 5489, 6018, 6580, 7176, 7807, 8474, 9178, 9920, 10701, 11522, 12384, 13288, 14235, 15226, 16262, 17344, 18473, 19650, 20876, 22152, 23479, 24858, 26290, 27776, 29317, 30914, 32568, 34280, 36051, 37882, 39774, 41728, 43745, 45826, 47972, 50184, 52463, 54810, 57226, 59712, 62269, 64898, 67600, 70376, 73227, 76154, 79158, 82240, 85401, 88642, 91964, 95368, 98855, 102426, 106082, 109824, 113653, 117570, 121576, 125672, 129859, 134138, 138510, 142976, 147537, 152194, 156948, 161800, 166751, 171802, 176954, 182208, 187565, 193026, 198592, 204264, 210043, 215930, 221926, 228032, 234249, 240578, 247020, 253576, 260247, 267034, 273938, 280960, 288101, 295362, 302744, 310248, 317875, 325626, 333502, 341504, 349633, 357890, 366276, 374792, 383439, 392218, 401130, 410176, 419357, 428674, 438128, 447720, 457451, 467322, 477334, 487488, 497785, 508226, 518812, 529544, 540423, 551450, 562626, 573952, 585429, 597058, 608840, 620776, 632867, 645114, 657518, 670080, 682801, 695682, 708724, 721928, 735295, 748826, 762522, 776384, 790413, 804610, 818976, 833512, 848219, 863098, 878150, 893376, 908777, 924354, 940108, 956040, 972151, 988442, 1004914, 1021568, 1038405, 1055426, 1072632, 1090024, 1107603, 1125370, 1143326, 1161472, 1179809, 1198338, 1217060, 1235976, 1255087, 1274394, 1293898, 1313600, 1333501, 1353602, 1373904, 1394408, 1415115, 1436026, 1457142, 1478464, 1499993, 1521730, 1543676, 1565832, 1588199, 1610778, 1633570, 1656576, 1679797, 1703234, 1726888, 1750760, 1774851, 1799162, 1823694, 1848448, 1873425, 1898626, 1924052, 1949704, 1975583, 2001690, 2028026, 2054592, 2081389, 2108418, 2135680, 2163176, 2190907, 2218874, 2247078, 2275520, 2304201, 2333122, 2362284, 2391688, 2421335, 2451226, 2481362, 2511744, 2542373, 2573250, 2604376, 2635752, 2667379, 2699258, 2731390, 2763776, 2796417, 2829314, 2862468, 2895880, 2929551, 2963482, 2997674, 3032128, 3066845, 3101826, 3137072, 3172584, 3208363, 3244410, 3280726, 3317312, 3354169, 3391298, 3428700, 3466376, 3504327, 3542554, 3581058, 3619840, 3658901, 3698242, 3737864, 3777768, 3817955, 3858426, 3899182, 3940224, 3981553, 4023170, 4065076, 4107272, 4149759, 4192538, 4235610, 4278976, 4322637, 4366594, 4410848, 4455400, 4500251, 4545402, 4590854, 4636608, 4682665, 4729026, 4775692, 4822664, 4869943, 4917530, 4965426, 5013632, 5062149, 5110978, 5160120, 5209576, 5259347, 5309434, 5359838, 5410560, 5461601, 5512962, 5564644, 5616648, 5668975, 5721626, 5774602, 5827904, 5881533, 5935490, 5989776, 6044392, 6099339, 6154618, 6210230, 6266176, 6322457, 6379074, 6436028, 6493320, 6550951, 6608922, 6667234, 6725888, 6784885, 6844226, 6903912, 6963944, 7024323, 7085050, 7146126, 7207552, 7269329, 7331458, 7393940, 7456776, 7519967, 7583514, 7647418, 7711680, 7776301, 7841282, 7906624, 7972328, 8038395, 8104826, 8171622, 8238784, 8306313, 8374210, 8442476, 8511112, 8580119, 8649498, 8719250, 8789376, 8859877, 8930754, 9002008, 9073640, 9145651, 9218042, 9290814, 9363968, 9437505, 9511426, 9585732, 9660424, 9735503, 9810970, 9886826, 9963072, 10039709, 10116738, 10194160, 10271976, 10350187, 10428794, 10507798, 10587200, 10667001, 10747202, 10827804, 10908808, 10990215, 11072026, 11154242, 11236864, 11319893, 11403330, 11487176, 11571432, 11656099, 11741178, 11826670, 11912576, 11998897, 12085634, 12172788, 12260360, 12348351, 12436762, 12525594, 12614848, 12704525, 12794626, 12885152, 12976104, 13067483, 13159290, 13251526, 13344192, 13437289, 13530818, 13624780, 13719176, 13814007, 13909274, 14004978, 14101120, 14197701, 14294722, 14392184, 14490088, 14588435, 14687226, 14786462, 14886144, 14986273, 15086850, 15187876, 15289352, 15391279, 15493658, 15596490, 15699776, 15803517, 15907714, 16012368, 16117480, 16223051, 16329082, 16435574, 16542528, 16649945, 16757826, 16866172, 16974984, 17084263, 17194010, 17304226, 17414912, 17526069, 17637698, 17749800, 17862376, 17975427, 18088954, 18202958, 18317440, 18432401, 18547842, 18663764, 18780168, 18897055, 19014426, 19132282, 19250624, 19369453, 19488770, 19608576, 19728872, 19849659, 19970938, 20092710, 20214976, 20337737, 20460994, 20584748, 20709000, 20833751, 20959002, 21084754, 21211008, 21337765, 21465026, 21592792, 21721064, 21849843, 21979130, 22108926, 22239232, 22370049, 22501378, 22633220, 22765576, 22898447, 23031834, 23165738, 23300160, 23435101, 23570562, 23706544, 23843048, 23980075, 24117626, 24255702, 24394304, 24533433, 24673090, 24813276, 24953992, 25095239, 25237018, 25379330, 25522176, 25665557, 25809474, 25953928, 26098920, 26244451, 26390522, 26537134, 26684288, 26831985, 26980226, 27129012, 27278344, 27428223, 27578650, 27729626, 27881152, 28033229, 28185858, 28339040, 28492776, 28647067, 28801914, 28957318, 29113280, 29269801, 29426882, 29584524, 29742728, 29901495, 30060826, 30220722, 30381184, 30542213, 30703810, 30865976, 31028712, 31192019, 31355898, 31520350, 31685376, 31850977, 32017154, 32183908, 32351240, 32519151, 32687642, 32856714, 33026368, 33196605, 33367426, 33538832, 33710824, 33883403, 34056570, 34230326, 34404672, 34579609, 34755138, 34931260, 35107976, 35285287, 35463194, 35641698, 35820800.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 181713 values, from 1 to 999999021407449).

n\r 0  1 
213628445429 2 
3605706057260571 3 
468142227156814222714 4 
53634236343363433634236343 5 
6454271514445429151434542815142 6 
7259597787725959025959259590 7 
85678511358567851135711357113571135711357 8 
9201902019120191201902019120190201902019020190 9 
10272569086272589086272579086272579085272569086 10 
11165191652016520049558165190016520495570

A pictorial representation of the table above
motab
Imagine to divide the members of this family by a number n and compute the remainders. Should they be uniformly distributed, each remainder from 0 to n-1 would be obtained in about (1/n)-th of the cases. This outcome is represented by a white square. Reddish (resp. bluish) squares represent remainders which appear more (resp. less) frequently than 1/n.