A365975 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+1) / (3*k+1) ).

1, 1, 2, 6, 30, 180, 1260, 10800, 104760, 1130760, 13776480, 184044960, 2670220080, 42222280320, 718144004160, 13061603808000, 254036916144000, 5247117638294400, 114652672773408000, 2647321293055507200, 64330669872690566400, 1640738743703289331200

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (3*k)! * binomial(n,3*k+1) * a(n-3*k-1).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+1)/(3*k+1)))))

Crossrefs

Cf. A296676, A365976, A365977.

Sequence in context: A180897 A353184 A096769 * A111059 A009645 A274966

Adjacent sequences: A365972 A365973 A365974 * A365976 A365977 A365978

Keyword

nonn

Author

Seiichi Manyama, Sep 23 2023

Status

approved