A365898 Expansion of e.g.f. exp( Sum_{k>=0} x^(4*k+5) / (4*k+5)! ).

1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 126, 0, 0, 1, 2002, 126126, 0, 1, 32878, 11639628, 488864376, 1, 523754, 962159506, 164910249504, 5194672859377, 8390630, 79198593760, 44919303188760, 4895979169961881, 123378675217248882, 6434084214390, 11762691848427520

Offset: 0

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..609

Crossrefs

Cf. A057814, A365896, A365897.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\4, x^(4*k+5)/(4*k+5)!))))

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/4)} binomial(n-1,4*k+4) * a(n-4*k-5).

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