OFFSET
1,2
FORMULA
E.g.f.: -log(1 - exp(x) * x * (1 + 3*x + x^2)).
E.g.f.: -log(1 - Sum_{k>=1} k^3 * x^k / k!).
a(n) ~ (n-1)! / r^n, where r = 0.336491770414014560614859141224061461582454518... is the root of the equation exp(r)*r*(1 + 3*r + r^2) = 1. - Vaclav Kotesovec, Jul 11 2020
MATHEMATICA
a[n_] := a[n] = n^3 + (1/n) Sum[Binomial[n, k] k a[k] (n - k)^3, {k, 1, n - 1}]; Table[a[n], {n, 1, 19}]
nmax = 19; CoefficientList[Series[-Log[1 - Exp[x] x (1 + 3 x + x^2)], {x, 0, nmax}], x] Range[0, nmax]! // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 10 2020
STATUS
approved