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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

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

Cf. A007526, A053486, A066534, A348314.

Sequence in context: A055147 A014829 A048438 * A295602 A226199 A267637

Adjacent sequences:  A348309 A348310 A348311 * A348313 A348314 A348315

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Oct 11 2021

STATUS

approved

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Last modified May 18 23:31 EDT 2022. Contains 353826 sequences. (Running on oeis4.)