A357903 a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,k).

1, 0, 0, 1, 1, 1, 2, 4, 8, 17, 38, 89, 219, 567, 1543, 4400, 13094, 40507, 129874, 430731, 1476030, 5222544, 19066758, 71764369, 278166767, 1108986222, 4541765652, 19085377108, 82211094414, 362717859475, 1638071537802, 7567876937002, 35748311794246, 172558399424154

Offset

0,7

Links

Table of n, a(n) for n=0..33.

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\3, stirling(n-2*k, 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)))

Crossrefs

Cf. A000110, A171367, A357904.

Sequence in context: A229202 A003007 A086615 * A081124 A340776 A090901

Adjacent sequences: A357900 A357901 A357902 * A357904 A357905 A357906

Keyword

nonn

Author

Seiichi Manyama, Oct 19 2022

Status

approved