A353261 Expansion of Sum_{k>=0} (-2)^k * x^(2*k)/Product_{j=1..k} (1 - j * x).

1, 0, -2, -2, 2, 10, 18, 10, -62, -310, -894, -1590, 642, 21514, 120322, 461130, 1230466, 877194, -16158974, -142301750, -798423166, -3397990646, -9764986878, 2009650762, 294960691330, 2788851766154, 18403159253250, 95083470290634, 350847712602498

Offset: 0

Author

Seiichi Manyama, Apr 09 2022

Keywords

• sign

Crossrefs

Cf. A097341, A097342, A171367, A353260.

Cf. A353254.

Programs

Mathematica

a[n_] := Sum[(-2)^k * StirlingS2[n - k, k], {k, 0, Floor[n/2]}]; Array[a, 30, 0] (* Amiram Eldar, Apr 09 2022 *)

PARI

my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (-2)^k*x^(2*k)/prod(j=1, k, 1-j*x)))

PARI

a(n) = sum(k=0, n\2, (-2)^k*stirling(n-k, k, 2));

Formula

a(n) = Sum_{k=0..floor(n/2)} (-2)^k * Stirling2(n-k,k).