A038043 Number of ways to partition a labeled set into 2-colored subsets of equal size.

2, 4, 4, 10, 4, 54, 4, 284, 564, 2146, 4, 64068, 4, 273706, 3055056, 9322174, 4, 455865986, 4, 7379708912, 72557376324, 27499326586, 4, 28169911778038, 10389345718756, 15811717561854, 5955168301010504, 26845490776452304, 4

Offset

1,1

Links

Table of n, a(n) for n=1..29.

Formula

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

a(n) = 2 * A038041(n). - Sean A. Irvine, Jan 05 2021

Maple

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:

Prog

(PARI) a(n) = sumdiv(n, d, ((2*n!)/(d!*((n/d)!)^d))); \\ Michel Marcus, Jan 05 2021

Crossrefs

Cf. A038041.

Sequence in context: A253827 A186987 A300549 * A126138 A366575 A363641

Adjacent sequences: A038040 A038041 A038042 * A038044 A038045 A038046

Keyword

nonn

Author

Christian G. Bower

Extensions

More terms from James Sellers, Feb 19 2001

Status

approved