OFFSET
0,2
FORMULA
a(0) = 1; a(n) = n * a(n-1) + Sum_{k=1..n} binomial(n,k) * 4^(k-1) * a(n-k).
a(n) ~ n! / ((1 + LambertW(exp(5))) * ((5 - LambertW(exp(5)))/4)^(n+1)). - Vaclav Kotesovec, Jun 19 2022
MATHEMATICA
nmax = 18; CoefficientList[Series[4/(5 - 4 x - Exp[4 x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 1; a[n_] := a[n] = n a[n - 1] + Sum[Binomial[n, k] 4^(k - 1) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 18}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 19 2022
STATUS
approved