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

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A296676, A365976, A365977.

Programs

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)))))

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).