A335577 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * k^2 * a(n-k).

1, -1, -2, 9, 32, -285, -1236, 18725, 86176, -2087001, -9204580, 351964569, 1336442304, -83422970917, -231889447076, 26389118293005, 35917342192064, -10722110983670193, 5028963509133756, 5432569724760331841, -14852185163192897120, -3352369390318855889661

Offset: 0

Author

Ilya Gutkovskiy, Jan 26 2021

Keywords

• sign

Crossrefs

Cf. A302189, A302397, A308861, A316087, A335578.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] k^2 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 21}]
nmax = 21; CoefficientList[Series[1/(1 + Exp[x] x (1 + x)), {x, 0, nmax}], x] Range[0, nmax]!

Formula

E.g.f.: 1 / (1 + exp(x) * x * (1 + x)).

E.g.f.: 1 / (1 + Sum_{k>=1} k^2 * x^k / k!).