A335578 a(0) = 1; a(n) = -Sum_{k=1..n} binomial(n,k) * k^3 * a(n-k).
1, -1, -6, 15, 272, -745, -29976, 61271, 6065856, -2723697, -1941455080, -3989345041, 897021218400, 4964061925511, -562221881675832, -5689641396555705, 456732442022509184, 7321841133968133023, -464200472167634521800, -10961686347887871324289, 573373115861405030522400
Offset: 0
Keywords
Programs
-
Mathematica
a[0] = 1; a[n_] := a[n] = -Sum[Binomial[n, k] k^3 a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}] nmax = 20; CoefficientList[Series[1/(1 + Exp[x] x (1 + 3 x + x^2)), {x, 0, nmax}], x] Range[0, nmax]!
Formula
E.g.f.: 1 / (1 + exp(x) * x * (1 + 3*x + x^2)).
E.g.f.: 1 / (1 + Sum_{k>=1} k^3 * x^k / k!).