A108953 Convolution of 3^n*n! and n!.

1, 4, 23, 192, 2184, 31728, 560412, 11630592, 276921216, 7433925120, 222038547840, 7301712936960, 262112637864960, 10198096116526080, 427456901317420800, 19202256562264473600, 920321900537337446400, 46874495077202077286400, 2528269620326135923507200

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f. (for offset 1): log(1-4x+3x^2)/((3x-4)).

a(n) = n!*Sum_{k=0..n} 3^k/binomial(n, k).

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

a(n) ~ 3^n * n! * (1 + 1/(3*n) + 2/(9*n^2) + 4/(9*n^3) + 32/(27*n^4) + 328/(81*n^5) + 152/(9*n^6) + 20168/(243*n^7) + 341944/(729*n^8) + 2183512/(729*n^9) + 15540472/(729*n^10) + ...). - Vaclav Kotesovec, Dec 07 2020

Mathematica

Rest[Range[0, 20]! CoefficientList[Series[((Log[1 - 4 x + 3 x^2]))/(3 x - 4), {x, 0, 20}], x]] (* Vincenzo Librandi, Jul 13 2015 *)

Crossrefs

Cf. A107713, A110467.

Sequence in context: A292971 A317967 A186117 * A369140 A222454 A336948

Adjacent sequences: A108950 A108951 A108952 * A108954 A108955 A108956

Keyword

easy,nonn

Author

Paul Barry, Jul 21 2005

Extensions

More terms from Vincenzo Librandi, Jul 13 2015

Status

approved