A357925 a(n) = Sum_{k=0..floor(n/3)} Stirling2(n - 2*k,n - 3*k).

1, 1, 1, 1, 2, 4, 7, 12, 23, 47, 95, 192, 402, 869, 1898, 4181, 9379, 21431, 49556, 115770, 273919, 656476, 1590061, 3888783, 9608337, 23980678, 60402964, 153469477, 393325442, 1016628823, 2648842279, 6955029849, 18400676786, 49042936328, 131646082259

Offset

0,5

Links

Table of n, a(n) for n=0..34.

Formula

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

Mathematica

Table[Sum[StirlingS2[n-2k, n-3k], {k, 0, Floor[n/3]}], {n, 0, 40}] (* Harvey P. Dale, Feb 22 2024 *)

Prog

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

Crossrefs

Cf. A024428, A357926.

Cf. A357903.

Sequence in context: A226160 A018181 A141017 * A190591 A332338 A332836

Adjacent sequences: A357922 A357923 A357924 * A357926 A357927 A357928

Keyword

nonn

Author

Seiichi Manyama, Oct 20 2022

Status

approved