OFFSET
0,4
FORMULA
a(0) = 1; a(n) = (n-1)! * Sum_{k=2..n} k * 2^(k-3)/(k-1) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/2)} 2^(n-3*k) * |Stirling1(n-k,k)|/(n-k)!.
a(n) ~ sqrt(Pi) * 2^(n + 1/2) * n^(n - 3/8) / (Gamma(1/8) * exp(n)). - Vaclav Kotesovec, Mar 14 2024
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-2*x)^(x/4)))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=2, i, j*2^(j-3)/(j-1)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\2, 2^(n-3*k)*abs(stirling(n-k, k, 1))/(n-k)!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 24 2022
STATUS
approved