A353289 a(n) = Sum_{k=0..floor(n/2)} (n-k)^k * |Stirling1(n-k,k)|.

1, 0, 1, 2, 10, 51, 323, 2354, 19535, 181606, 1869549, 21110063, 259400501, 3445913273, 49207968328, 751698726580, 12231484211240, 211208935989003, 3857425360784596, 74292198980174828, 1504832580013205275, 31980327844846620785, 711498612995378484414

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

Prog

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

Crossrefs

Cf. A343579, A352802, A353252.

Cf. A132393, A353290.

Sequence in context: A019476 A019475 A020042 * A307208 A075436 A319325

Adjacent sequences: A353286 A353287 A353288 * A353290 A353291 A353292

Keyword

nonn

Author

Seiichi Manyama, Apr 09 2022

Status

approved