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Eulerian numbers

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Numbers which count the permutations with a given number of ascents. more

The Eulerian numbers up to 1015 :
1, 4, 11, 26, 57, 66, 120, 247, 302, 502, 1013, 1191, 2036, 2416, 4083, 4293, 8178, 14608, 15619, 16369, 32752, 47840, 65519, 88234, 131054, 152637, 156190, 262125, 455192, 478271, 524268, 1048555, 1310354, 1479726, 2097130, 2203488, 4194281, 4537314, 8388584, 9738114, 10187685, 13824739, 15724248, 16777191, 33554406, 41932745, 45533450, 66318474, 67108837, 126781020, 134217700, 162512286, 198410786, 268435427, 382439924, 423281535, 536870882, 848090912, 1073741793, 1151775897, 1505621508, 2147483616, 2275172004, 2571742175, 3464764515, 3572085255, 4294967263, 8589934558, 10414216090, 12843262863, 14875399450, 15041229521, 17179869149, 27971176092, 31284590870, 34359738332, 61403313100, 68719476699, 85383238549, 93941852511, 102776998928, 137438953434, 251732291184, 274877906905, 282010106381, 311387598411, 447538817472, 473353301060, 549755813848, 782115518299, 846416194536, 1026509354985, 1099511627735, 2199023255510, 2540053889352, 2575022097600, 3207483178157, 4168403181210, 4398046511061, 5717291972382, 6382798925475, 7621839388981, 8796093022164, 13796160184500, 16871482830550, 17592186044371, 22869007827143, 31055652948388, 35184372088786, 40457344748072, 68111623139600, 68614271237958, 70368744177617, 73008517581444, 83137223185370, 114890380658550, 140737488355280, 205857846098570, 274419271461131, 278794377854832, 281474976710607, 285997074307300, 382493246941965, 562949953421262, 617604676807707.

Distribution of the remainders when the numbers in this family are divided by n=2, 3,..., 11. (I took into account 76701 values, from 1 to 101000).

n\r 0  1 
26386312838 2 
35829392249184 3 
4516286373122356465 4 
5496907788611961546950 5 
64968720707022860671542162 6 
745832637946275167457644245696 7 
83898631476300322312642322659353242 8 
9380283629281810163266631741010229293192 9 
1043433205946511328522462575729146848261726 10 
11362714765402138923796407240453524370539354675

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.