A365978 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(3*k+2) / (3*k+2) ).

1, 0, 1, 0, 6, 24, 90, 1008, 7560, 54432, 712152, 7620480, 81130896, 1266632640, 17587441872, 246734377344, 4527397929600, 77238618702336, 1340945212763520, 28407941067018240, 574640938744314624, 11868502219930137600, 285787326567523173120

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A226226, A365979.

Cf. A365908.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\3, x^(3*k+2)/(3*k+2)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-2)/3)} (3*k+1)! * binomial(n,3*k+2) * a(n-3*k-2).