A353256 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (3 * j + x).

1, 0, 1, 3, 19, 171, 2044, 30528, 547390, 11457237, 274198402, 7385438214, 221099038597, 7282925988615, 261763288109884, 10194190355448399, 427609812103844122, 19220373155515189149, 921621193002227307943, 46958377673245988620737

Offset

0,4

Links

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

Formula

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

Mathematica

a[n_] := Sum[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, 3^(n-2*k)*abs(stirling(n-k, k, 1)));

Crossrefs

Cf. A353255, A353257, A353258.

Cf. A353262.

Sequence in context: A080894 A143768 A256493 * A275283 A349768 A083071

Adjacent sequences: A353253 A353254 A353255 * A353257 A353258 A353259

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2022

Status

approved