A053491 Expansion of e.g.f. (1-2*x)^(-x).

1, 0, 4, 12, 112, 960, 10848, 141120, 2122496, 36094464, 685578240, 14385761280, 330532435968, 8253827112960, 222587077558272, 6447285982126080, 199630453605335040, 6580280144225894400, 230056747973625249792, 8503148524089755566080

Offset: 0

Author

N. J. A. Sloane, Jan 15 2000

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A007113, A053489, A066166.

Programs

Mathematica

CoefficientList[Series[(1-2x)^(-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

PARI

a(n) = n!*sum(k=0, n\2, 2^(n-k)*abs(stirling(n-k, k, 1))/(n-k)!); \\ Seiichi Manyama, May 20 2022

Formula

a(n) ~ 2^(n+1/2)*n^n/exp(n). - Vaclav Kotesovec, Jun 27 2013

a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-k) * |Stirling1(n-k,k)|/(n-k)!. - Seiichi Manyama, May 20 2022