OFFSET
0,2
FORMULA
E.g.f.: 1 / (1 - 3*x + log(1 - x)).
a(n) ~ n! / ((3/c + 2 - c) * (1 - c/3)^n), where c = LambertW(3*exp(2)) = 2.2761339297716461777892556270138... - Vaclav Kotesovec, Apr 26 2021
MATHEMATICA
a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] (n - k - 1)! a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[1/(1 - 3 x + Log[1 - x]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 26 2021
STATUS
approved