OFFSET
0,3
FORMULA
E.g.f.: 1 / (exp(x) * (4 - 5*x) - 3).
a(n) ~ n! * c / (3*(1-c) * (4/5 - c)^(n+1)), where c = -LambertW(-3*exp(-4/5)/5). - Vaclav Kotesovec, Aug 31 2020
MATHEMATICA
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] (5 k - 4) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 19}]
nmax = 19; CoefficientList[Series[1/(Exp[x] (4 - 5 x) - 3), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) seq(n)={Vec(serlaplace(1 / (exp(x + O(x*x^n)) * (4 - 5*x) - 3)))} \\ Andrew Howroyd, Aug 31 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 31 2020
STATUS
approved