A365911 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+3) / (4*k+3)! ).

1, 0, 0, 1, 0, 0, 20, 1, 0, 1680, 240, 1, 369600, 102960, 4160, 168168001, 76876800, 7743840, 137225153280, 93117024001, 17091609600, 182510023324320, 172080261401600, 49615854288001, 369403226582016000, 461748751736204400, 191552892427653120

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..498

Crossrefs

Cf. A102233, A332258, A365912.

Cf. A352429, A365917.

Cf. A307978.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(sinh(x)-sin(x))/2)))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/4)} binomial(n,4*k+3) * a(n-4*k-3).

E.g.f.: 1 / ( 1 - (sinh(x) - sin(x))/2 ).