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binomial coefficient  and  Hogben n.

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(max 15 digits)

First numbers that belong to both sets:

21, 91, 703, 3081, 23871, 104653, 810901, 3555111, 27546753, 120769111, 935778691, 4102594653, 31788928731, 139367449081, 1079887798153, 4734390674091.