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 A069015 #18 May 22 2025 07:40:35
%S A069015 1,7,65,786,11814,212772,4468932,107259408,2896044336,86881692960,
%T A069015 2867099496480,103215621790080,4025409728814720,169067214837239040,
%U A069015 7608024754854048000,365185189540668672000,18624444687496892160000
%N A069015 a(n) = n! * 3^n * Sum_{i=1..n} 1/(i * 3^i).
%F A069015 E.g.f.: -log(1-x)/(1-3*x). - _Vladeta Jovovic_, Feb 07 2003
%F A069015 a(n) ~ n! * 3^n * log(3/2). - _Vaclav Kotesovec_, Oct 05 2013
%F A069015 From _Seiichi Manyama_, May 22 2025: (Start)
%F A069015 a(n) = 3 * n * a(n-1) + (n-1)!.
%F A069015 a(n) = (4*n-1) * a(n-1) - 3 * (n-1)^2 * a(n-2). (End)
%t A069015 Rest[CoefficientList[Series[-Log[1-x]/(1-3*x), {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, Oct 05 2013 *)
%Y A069015 Cf. A000254, A068102.
%K A069015 easy,nonn
%O A069015 1,2
%A A069015 _Benoit Cloitre_, Apr 14 2002