A353255 Expansion of Sum_{k>=0} x^k * Product_{j=0..k-1} (2 * j + x).

1, 0, 1, 2, 9, 54, 429, 4252, 50605, 703388, 11184597, 200247446, 3986363597, 87343744490, 2088739037209, 54134344486296, 1511446306795417, 45227224242345336, 1443916049346447913, 48989635949583331658, 1760229264304229244753, 66770472164443344587550

Offset

0,4

Links

Table of n, a(n) for n=0..21.

Formula

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

Mathematica

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

Crossrefs

Cf. A353256, A353257, A353258.

Sequence in context: A222014 A321974 A127128 * A254795 A064151 A075679

Adjacent sequences: A353252 A353253 A353254 * A353256 A353257 A353258

Keyword

nonn

Author

Seiichi Manyama, Apr 08 2022

Status

approved