OFFSET
0,2
FORMULA
E.g.f.: (1 + x)^2 * exp(x + x^2).
a(n) = -(n-4)*a(n-1) + 3*(n-1)*a(n-2) + 2*(n-1)*(n-2)*a(n-3) for n > 2.
a(n) = ((n^2-7*n+3)*a(n-1) + 2*(n-1)*(n^2-3*n-1)*a(n-2))/(n^2-5*n+3) for n > 1.
a(n) ~ n^(n/2 + 1) * 2^(n/2 - 3/2) / exp(1/8 - sqrt(n/2) + n/2) * (1 + 157/(48*sqrt(2*n))). - Vaclav Kotesovec, Nov 12 2024
PROG
(PARI) a(n) = n!*sum(k=0, n, binomial(k+2, n-k)/k!);
CROSSREFS
KEYWORD
nonn,easy,new
AUTHOR
Seiichi Manyama, Nov 12 2024
STATUS
approved