A354264 Expansion of e.g.f. 1/(1 + 4 * log(1-x)).

1, 4, 36, 488, 8824, 199456, 5410208, 171209664, 6192052800, 251937937920, 11389639660032, 566394573855744, 30726758349800448, 1805828538127687680, 114293350061315678208, 7750480651439579529216, 560615413313367534698496, 43085423893717998388740096

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

E.g.f.: 1/(1 + 4 * log(1-x)).

a(0) = 1; a(n) = 4 * Sum_{k=1..n} (k-1)! * binomial(n,k) * a(n-k).

a(n) = Sum_{k=0..n} 4^k * k! * |Stirling1(n, k)|.

a(n) ~ n! * exp(n/4) / (4 * (exp(1/4) - 1)^(n+1)). - Vaclav Kotesovec, Jun 04 2022

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(1+4*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=4*sum(j=1, i, (j-1)!*binomial(i, j)*v[i-j+1])); v;
(PARI) a(n) = sum(k=0, n, 4^k*k!*abs(stirling(n, k, 1)));

Crossrefs

Column k=4 of A320079.

Cf. A094417, A354147, A354241.

Sequence in context: A370927 A094417 A349504 * A138435 A366337 A008546

Adjacent sequences: A354261 A354262 A354263 * A354265 A354266 A354267

Keyword

nonn

Author

Seiichi Manyama, May 21 2022

Status

approved