OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} rf(n - k + 1, k)*k^2, where rf is the rising factorial.
a(n) = (2 + n*(n + 2))*a(n - 1)/(n - 1) - (n + 1)*a(n - 2) for n >= 3.
A002775(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*a(k).
MAPLE
egf := -x*(x + 1)*exp(x)/(x - 1)^3: ser := series(egf, x, 32):
seq(n!*coeff(ser, x, n), n = 0..20);
MATHEMATICA
a[n_] := Sum[Pochhammer[n - k + 1, k]*k^2, {k, 0, n}];
Table[a[n], {n, 0, 20}]
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Apr 20 2021
STATUS
approved