This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A108953 #13 Dec 07 2020 17:29:09
%S A108953 1,4,23,192,2184,31728,560412,11630592,276921216,7433925120,
%T A108953 222038547840,7301712936960,262112637864960,10198096116526080,
%U A108953 427456901317420800,19202256562264473600,920321900537337446400,46874495077202077286400,2528269620326135923507200
%N A108953 Convolution of 3^n*n! and n!.
%F A108953 E.g.f. (for offset 1): log(1-4x+3x^2)/((3x-4)).
%F A108953 a(n) = n!*Sum_{k=0..n} 3^k/binomial(n, k).
%F A108953 a(n) = Sum_{k=0..n} k!*3^k*(n-k)!.
%F A108953 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
%t A108953 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 *)
%Y A108953 Cf. A107713, A110467.
%K A108953 easy,nonn
%O A108953 0,2
%A A108953 _Paul Barry_, Jul 21 2005
%E A108953 More terms from _Vincenzo Librandi_, Jul 13 2015