A357939 a(n) = Sum_{k=0..floor(n/2)} Stirling2(k,n - 2*k).

1, 0, 0, 1, 0, 1, 1, 1, 3, 2, 7, 7, 16, 26, 41, 92, 128, 317, 478, 1107, 1977, 4077, 8547, 16310, 37775, 71489, 170660, 339138, 795833, 1705058, 3876254, 8926023, 19888522, 48187837, 107726407, 267597455, 613509355, 1531527270, 3646775589, 9066267823

Offset

0,9

Links

Table of n, a(n) for n=0..39.

Formula

G.f.: Sum_{k>=0} x^(3*k)/Product_{j=1..k} (1 - j * x^2).

Prog

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

Crossrefs

Cf. A357940, A357941.

Cf. A357903.

Sequence in context: A324876 A226370 A054183 * A188656 A210204 A208657

Adjacent sequences: A357936 A357937 A357938 * A357940 A357941 A357942

Keyword

nonn

Author

Seiichi Manyama, Oct 21 2022

Status

approved