OFFSET
0,5
FORMULA
a(n) = n! * Sum_{k=0..floor(n/4)} (2*k)! * Stirling2(n-2*k,2*k)/(4^k * (n-2*k)!).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-(x*(exp(x)-1))^2/4)))
(PARI) a(n) = n!*sum(k=0, n\4, (2*k)!*stirling(n-2*k, 2*k, 2)/(4^k*(n-2*k)!));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 09 2022
STATUS
approved