A353290 a(n) = Sum_{k=0..floor(n/2)} (n-k)^(n-2*k) * |Stirling1(n-k,k)|.

1, 0, 1, 2, 19, 393, 15177, 939394, 85063260, 10599342278, 1739073390797, 363404567436467, 94224446795779884, 29683590039199285223, 11167286542016941966714, 4945143125245884296040780, 2546112368234517215955646341, 1508197687055444623135714912377

Offset

0,4

Links

Table of n, a(n) for n=0..17.

Formula

G.f.: Sum_{k>=0} x^k * Product_{j=0..k-1} (k * j + x).

Prog

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

Crossrefs

Cf. A343579, A353255, A353256.

Cf. A353289.

Sequence in context: A110818 A325288 A155927 * A332967 A120420 A350939

Adjacent sequences: A353287 A353288 A353289 * A353291 A353292 A353293

Keyword

nonn

Author

Seiichi Manyama, Apr 09 2022

Status

approved