A365896 Expansion of e.g.f. exp( Sum_{k>=0} x^(2*k+5) / (2*k+5)! ).

1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 126, 1, 792, 1, 3718, 126127, 15808, 2450449, 64702, 31593277, 489125360, 343746937, 21511079558, 3435303323, 588969369056, 5227461790937, 13006203613950, 434431246754441, 255046847579760, 21684989820772201, 128034458842091862

Offset

0,11

Links

Seiichi Manyama, Table of n, a(n) for n = 0..599

Formula

a(0) = 1; a(n) = Sum_{k=0..floor((n-5)/2)} binomial(n-1,2*k+4) * a(n-2*k-5).

E.g.f.: exp( -x - x^3/6 + sinh(x) ).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\2, x^(2*k+5)/(2*k+5)!))))

Crossrefs

Cf. A057814, A365897, A365898.

Sequence in context: A365897 A050451 A059024 * A331401 A267199 A348898

Adjacent sequences: A365893 A365894 A365895 * A365897 A365898 A365899

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2023

Status

approved