A353258 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (3 * j - x).

1, 0, -1, -3, -17, -153, -1846, -27828, -503000, -10599873, -255143728, -6906078108, -207627211745, -6864486246225, -247526246562328, -9667515778323735, -406560434763167342, -18316445888374834635, -880110629723965618045, -44928348211160605056537

Offset

0,4

Links

Table of n, a(n) for n=0..19.

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * 3^(n-2*k) * |Stirling1(n-k,k)|.

Mathematica

a[n_] := Sum[(-1)^k * 3^(n - 2*k) * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 20, 0] (* Amiram Eldar, Apr 09 2022 *)

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, 3*j-x)))
(PARI) a(n) = sum(k=0, n\2, (-1)^k*3^(n-2*k)*abs(stirling(n-k, k, 1)));

Crossrefs

Cf. A353255, A353256, A353257.

Sequence in context: A193161 A364630 A318987 * A208832 A135751 A368444

Adjacent sequences: A353255 A353256 A353257 * A353259 A353260 A353261

Keyword

sign

Author

Seiichi Manyama, Apr 08 2022

Status

approved