A357940 a(n) = Sum_{k=0..floor(n/3)} Stirling2(k,n - 3*k).

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 3, 1, 1, 7, 6, 2, 15, 25, 11, 32, 90, 66, 78, 302, 351, 267, 987, 1703, 1305, 3291, 7799, 7463, 11976, 34568, 43584, 51329, 151631, 249527, 266058, 675490, 1395375, 1586432, 3159982, 7675720, 10132557, 16108875, 41991096, 66170977, 91724556

Offset

0,12

Links

Table of n, a(n) for n=0..49.

Formula

G.f.: Sum_{k>=0} x^(4*k)/Product_{j=1..k} (1 - j * x^3).

Prog

(PARI) a(n) = sum(k=0, n\3, stirling(k, n-3*k, 2));
(PARI) my(N=50, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k)/prod(j=1, k, 1-j*x^3)))

Crossrefs

Cf. A357939, A357941.

Cf. A357904, A357925.

Sequence in context: A263858 A263862 A263861 * A133800 A146900 A132733

Adjacent sequences: A357937 A357938 A357939 * A357941 A357942 A357943

Keyword

nonn

Author

Seiichi Manyama, Oct 21 2022

Status

approved