A368555 - OEIS

A368555

a(n) = Sum_{k=0..n} k! * 3^(n-k).

1, 4, 14, 48, 168, 624, 2592, 12816, 78768, 599184, 5426352, 56195856, 647589168, 8169788304, 111687656112, 1642737336336, 25851001897008, 433240433787024, 7702095007089072, 144751385430099216, 2867156164466937648, 59692410665110252944

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(0) = 1; a(n) = 3*a(n-1) + n!.

a(n) = (n+3)*a(n-1) - 3*n*a(n-2).

a(n) ~ n!. - Vaclav Kotesovec, Jan 13 2024

PROG

(PARI) a(n) = sum(k=0, n, k!*3^(n-k));

CROSSREFS

Cf. A003422, A058006, A112370, A112541, A233449.

Sequence in context: A082590 A085280 A007851 * A014325 A047028 A220819

Adjacent sequences: A368552 A368553 A368554 * A368556 A368557 A368558

KEYWORD

nonn,easy

AUTHOR

Seiichi Manyama, Dec 29 2023

STATUS

approved