OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 21 2022
STATUS
approved