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A343673
a(0) = 1; a(n) = 3 * n * a(n-1) + Sum_{k=0..n-1} binomial(n,k) * a(k).
4
1, 4, 33, 409, 6759, 139621, 3460989, 100091335, 3308146179, 123005753041, 5081871122073, 230948185830187, 11449697796242319, 614944043618257237, 35568197580789653685, 2204201734650777596863, 145703352769994600516187, 10233323176300508748808921, 761004837938469796089586257
OFFSET
0,2
FORMULA
E.g.f.: 1 / (2 - 3*x - exp(x)).
a(n) ~ n! * 3^n / ((1 + LambertW(exp(2/3)/3)) * (2 - 3*LambertW(exp(2/3)/3))^(n+1)). - Vaclav Kotesovec, Jun 20 2022
MATHEMATICA
a[0] = 1; a[n_] := a[n] = 3 n a[n - 1] + Sum[Binomial[n, k] a[k], {k, 0, n - 1}]; Table[a[n], {n, 0, 18}]
nmax = 18; CoefficientList[Series[1/(2 - 3 x - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 25 2021
STATUS
approved