A365338 Expansion of e.g.f. exp( Sum_{k>=0} x^(3*k+2) / (3*k+2)! ).

1, 0, 1, 0, 3, 1, 15, 21, 106, 378, 1116, 6931, 20196, 136500, 558559, 3103191, 18524418, 90852217, 661904622, 3569749659, 25657118047, 171935108541, 1149965503347, 9166884110308, 62758177512570, 525194926694256, 4072360499426311, 33295056117878646

Offset

0,5

Links

Table of n, a(n) for n=0..27.

Formula

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\3, x^(3*k+2)/(3*k+2)!))))

Crossrefs

Cf. A000296, A365419.

Sequence in context: A263632 A284861 A284234 * A089278 A213245 A053485

Adjacent sequences: A365335 A365336 A365337 * A365339 A365340 A365341

Keyword

nonn

Author

Seiichi Manyama, Sep 22 2023

Status

approved