A365981 Expansion of e.g.f. 1 / ( 1 - Sum_{k>=0} x^(4*k+3) / (4*k+3) ).

1, 0, 0, 2, 0, 0, 80, 720, 0, 13440, 345600, 3628800, 5913600, 296524800, 7062681600, 92559667200, 442810368000, 18037334016000, 459627769036800, 7475081822208000, 65867064606720000, 2634706112643072000, 74102151110787072000, 1464478283948359680000

Offset: 0

Author

Seiichi Manyama, Sep 24 2023

Keywords

• nonn

Crossrefs

Cf. A355284, A365980, A365982.

Cf. A365911.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=0, N\4, x^(4*k+3)/(4*k+3)))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-3)/4)} (4*k+2)! * binomial(n,4*k+3) * a(n-4*k-3).