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