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A368767
a(n) = n! * (1 + Sum_{k=0..n} (-1)^k * binomial(k+2,3) / k!).
4
1, 0, 4, 2, 28, 105, 686, 4718, 37864, 340611, 3406330, 37469344, 449632492, 5845221941, 81833107734, 1227496615330, 19639945846096, 333879079382663, 6009823428889074, 114186645148891076, 2283732902977823060, 47958390962534282489, 1055084601175754216782
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