A365979 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(5*k+2) / (5*k+2) ).

1, 0, 1, 0, 6, 0, 90, 720, 2520, 51840, 113400, 4276800, 47401200, 444787200, 9725086800, 58378320000, 2029897584000, 30450131712000, 475261239024000, 11952610750080000, 127796530736160000, 4683810971473920000, 90707397988727520000, 1964217505623310080000

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A226226, A365978.

Cf. A365909.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\5, x^(5*k+2)/(5*k+2)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-2)/5)} (5*k+1)! * binomial(n,5*k+2) * a(n-5*k-2).