A352802 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (j + 3 * x).

1, 0, 3, 3, 15, 45, 198, 972, 5652, 37881, 289548, 2492640, 23906475, 253012653, 2930556024, 36883817127, 501315357690, 7318715960511, 114224260779891, 1897913866979529, 33449523840512127, 623265596538965334, 12241892922194658510, 252793167644378784006

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..451

Formula

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

Mathematica

a[n_] := Sum[3^k * Abs[StirlingS1[n - k, k]], {k, 0, Floor[n/2]}]; Array[a, 25, 0] (* Amiram Eldar, Apr 09 2022 *)

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^k*prod(j=0, k-1, j+3*x)))
(PARI) a(n) = sum(k=0, n\2, 3^k*abs(stirling(n-k, k, 1)));

Crossrefs

Cf. A343579, A353252, A353253, A353254.

Cf. A097342.

Sequence in context: A056314 A171379 A078631 * A160639 A280781 A046983

Adjacent sequences: A352799 A352800 A352801 * A352803 A352804 A352805

Keyword

nonn

Author

Seiichi Manyama, Apr 09 2022

Status

approved