OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..450
FORMULA
a(0) = 1; a(n) = ((n-1)!/2) * Sum_{k=3..n} k/(k-2) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/3)} |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).
a(n) ~ sqrt(2) * n^n / exp(n). - Vaclav Kotesovec, May 04 2022
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x)^(-x^2/2)))
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-x^2/2*log(1-x))))
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!/2*sum(j=3, i, j/(j-2)*v[i-j+1]/(i-j)!)); v;
(PARI) a(n) = n!*sum(k=0, n\3, abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 02 2022
STATUS
approved