A355719 Expansion of e.g.f. exp( x/(1 - log(1+x)) ).

1, 1, 3, 10, 45, 231, 1405, 9472, 72177, 596845, 5442631, 53052726, 561826309, 6286949787, 75704999721, 954108249676, 12862823623393, 179921659771257, 2683989118991467, 41178997678745506, 673670267643931581, 11223738258484213519, 200027545794685345749

Offset

0,3

Comments

a(43) is negative. - Vaclav Kotesovec, Jul 15 2022

Links

Table of n, a(n) for n=0..22.

Formula

a(0) = 1; a(n) = Sum_{k=1..n} A108125(k) * binomial(n-1,k-1) * a(n-k).

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(x/(1-log(1+x)))))
(PARI) a006252(n) = sum(k=0, n, k!*stirling(n, k, 1));
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*a006252(j-1)*binomial(i-1, j-1)*v[i-j+1])); v;

Crossrefs

Cf. A355718, A355720.

Cf. A006252, A108125.

Sequence in context: A346066 A211193 A134018 * A028417 A060311 A184947

Adjacent sequences: A355716 A355717 A355718 * A355720 A355721 A355722

Keyword

sign

Author

Seiichi Manyama, Jul 15 2022

Status

approved