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 A294190 #17 Aug 28 2025 07:07:58
%S A294190 1,9,117,1881,35505,763209,18309861,483213033,13876068609,
%T A294190 429885495945,14269174133301,504579048629049,18917482749919857,
%U A294190 748904109963227721,31194958415494252005,1363010131166317306569,62300347592864208824961
%N A294190 Expansion of e.g.f. exp(3*(1/(1-x)^3 - 1)).
%H A294190 Seiichi Manyama, <a href="/A294190/b294190.txt">Table of n, a(n) for n = 0..410</a>
%F A294190 E.g.f.: exp(3*(1/(1-x)^3 - 1)).
%F A294190 From _Vaclav Kotesovec_, Aug 28 2025: (Start)
%F A294190 a(n) = (4*n+5)*a(n-1) - 6*(n-2)*(n-1)*a(n-2) + 4*(n-3)*(n-2)*(n-1)*a(n-3) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-4).
%F A294190 a(n) ~ 3^(1/4) * exp(-9/4 + 5*sqrt(3)*n^(1/4)/8 + 3*sqrt(n)/2 + 4*n^(3/4)/sqrt(3) - n) * n^(n - 1/8)/2 * (1 + 1333*sqrt(3)/(2560*n^(1/4))). (End)
%t A294190 With[{nn=20},CoefficientList[Series[Exp[3(1/(1-x)^3-1)],{x,0,nn}],x] Range[ 0,nn]!] (* _Harvey P. Dale_, Mar 03 2018 *)
%o A294190 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(3*(1/(1-x)^3-1))))
%Y A294190 Column k=3 of A294188.
%Y A294190 Cf. A202826.
%K A294190 nonn,changed
%O A294190 0,2
%A A294190 _Seiichi Manyama_, Oct 24 2017