login
A348312
a(n) = n! * Sum_{k=0..n-1} 3^k / k!.
1
0, 1, 8, 51, 312, 1965, 13248, 97839, 800208, 7260921, 72806040, 801515979, 9620317512, 125071036389, 1751016829968, 26265324194055, 420245416687392, 7144172815479921, 128595113003161512, 2443307154421058019, 48866143111666389720, 1026189005418216656541, 22576158119430894214368
OFFSET
0,3
FORMULA
E.g.f.: x * exp(3*x) / (1 - x).
a(0) = 0; a(n) = n * (a(n-1) + 3^(n-1)).
a(n) ~ exp(3)*n!. - Stefano Spezia, Oct 11 2021
MATHEMATICA
Table[n! Sum[3^k/k!, {k, 0, n - 1}], {n, 0, 22}]
nmax = 22; CoefficientList[Series[x Exp[3 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]!
PROG
(PARI) a(n) = n!*sum(k=0, n-1, 3^k/k!); \\ Michel Marcus, Oct 11 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 11 2021
STATUS
approved