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

Author

Seiichi Manyama, Sep 22 2023

Keywords

• nonn

Crossrefs

Cf. A000296, A365419.

Programs

PARI

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

Formula

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