OFFSET
0,3
FORMULA
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (n-2*k)^k * (2*n-2*k)!/(2^k * k! * (n-2*k)!).
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x*exp(x^2/2)))/x))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*(2*n-2*k)!/(2^k*k!*(n-2*k)!))/(n+1);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 06 2024
STATUS
approved