OFFSET
0,2
FORMULA
E.g.f. A(x) satisfies A(x) = (1 + x*A(x))^2 * exp(x * A(x)).
a(n) = n! * Sum_{k=0..n} (n+1)^(k-1) * binomial(2*n+2,n-k)/k!.
a(n) ~ (2*(1 + sqrt(2)))^(n + 1/2) * n^(n-1) / exp((2 - sqrt(2))*n + 1 - sqrt(2)). - Vaclav Kotesovec, Nov 09 2024
PROG
(PARI) a(n) = n!*sum(k=0, n, (n+1)^(k-1)*binomial(2*n+2, n-k)/k!);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 09 2024
STATUS
approved