OFFSET
0,4
FORMULA
a(0) = 1; a(n) = (1/2) * Sum_{k=1..n} A052862(k) * binomial(n-1,k-1) * a(n-k).
a(n) ~ n! / (Gamma(log(2)/2) * 2^(log(2)/2) * n^(1 - log(2)/2) * log(2)^(n + log(2)/2)). - Vaclav Kotesovec, Jun 08 2022
MATHEMATICA
With[{nn=30}, CoefficientList[Series[1/(2-Exp[x])^(x/2), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Feb 12 2024 *)
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x))^(x/2)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*sum(k=1, j-1, (k-1)!*stirling(j-1, k, 2))*binomial(i-1, j-1)*v[i-j+1])/2); v;
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 25 2022
STATUS
approved