A365969 Expansion of e.g.f. exp( Sum_{k>=0} x^(5*k+1) / (5*k+1) ).

1, 1, 1, 1, 1, 1, 121, 841, 3361, 10081, 25201, 3684241, 50309281, 369738721, 1926648361, 7980936601, 1335634023361, 27705746752321, 302258931418081, 2283161710263841, 13419441405835201, 2498339829188508481, 70152448708746111961, 1025314852704395518441

Offset: 0

Author

Seiichi Manyama, Sep 23 2023

Keywords

• nonn

Crossrefs

Cf. A000246, A193437, A193438.

Cf. A333882, A365977.

Programs

PARI

my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(sum(k=0, N\5, x^(5*k+1)/(5*k+1)))))

Formula

a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/5)} a(n-5*k-1)/(n-5*k-1)!.

a(0) = a(1) = ... = a(4) = 1; a(n) = a(n-1) + 120 * binomial(n-1,5) * a(n-5).