A357904 a(n) = Sum_{k=0..floor(n/4)} Stirling2(n - 3*k,k).

1, 0, 0, 0, 1, 1, 1, 1, 2, 4, 8, 16, 33, 70, 153, 346, 814, 2000, 5138, 13776, 38395, 110695, 328638, 1001306, 3124626, 9978906, 32620854, 109225582, 374875483, 1319392590, 4761630252, 17610041358, 66668257846, 258018795970, 1019440760020, 4106982942054

Offset

0,9

Links

Table of n, a(n) for n=0..35.

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\4, stirling(n-3*k, k, 2));
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k)/prod(j=1, k, 1-j*x)))

Crossrefs

Cf. A000110, A171367, A357903.

Sequence in context: A317880 A299271 A110334 * A084636 A352044 A161869

Adjacent sequences: A357901 A357902 A357903 * A357905 A357906 A357907

Keyword

nonn

Author

Seiichi Manyama, Oct 19 2022

Status

approved