OFFSET
0,3
FORMULA
a(0) = 1; a(n) = n*a(n-1) + (-1)^n * binomial(n+2,3).
a(n) = n! + (-1)^n * A368585(n).
E.g.f.: (1 - x * (1-x+x^2/6) * exp(-x)) / (1-x).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace((1-x*sum(k=0, 2, binomial(2, k)*(-x)^k/(k+1)!)*exp(-x))/(1-x)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 04 2024
STATUS
approved