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Number of ways to partition a labeled set into 2-colored subsets of equal size.
0

%I #14 Jan 05 2021 05:05:25

%S 2,4,4,10,4,54,4,284,564,2146,4,64068,4,273706,3055056,9322174,4,

%T 455865986,4,7379708912,72557376324,27499326586,4,28169911778038,

%U 10389345718756,15811717561854,5955168301010504,26845490776452304,4

%N Number of ways to partition a labeled set into 2-colored subsets of equal size.

%F a(n) = Sum_{ d divides n } ((2*n!)/(d!*((n/d)!)^d)).

%F a(n) = 2 * A038041(n). - _Sean A. Irvine_, Jan 05 2021

%p with(numtheory): for n from 1 to 50 do d := divisors(n): s := 0: for k from 1 to nops(d) do s := s +(2*n!)/(d[k]!*((n/d[k])!)^d[k]) od: printf(`%d,`,s) od:

%o (PARI) a(n) = sumdiv(n, d, ((2*n!)/(d!*((n/d)!)^d))); \\ _Michel Marcus_, Jan 05 2021

%Y Cf. A038041.

%K nonn

%O 1,1

%A _Christian G. Bower_

%E More terms from _James A. Sellers_, Feb 19 2001