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 A294189 #16 Aug 28 2025 08:58:25
%S A294189 1,4,28,256,2848,37024,547936,9064192,165339904,3290839552,
%T A294189 70870959616,1640130678784,40555349598208,1066271901822976,
%U A294189 29684252411219968,871864036043259904,26931181039027879936,872418396180001718272,29564373329109844885504
%N A294189 E.g.f.: exp(2*(1/(1-x)^2 - 1)).
%H A294189 Seiichi Manyama, <a href="/A294189/b294189.txt">Table of n, a(n) for n = 0..427</a>
%F A294189 From _Vaclav Kotesovec_, Aug 28 2025: (Start)
%F A294189 a(n) = (3*n+1)*a(n-1) - 3*(n-2)*(n-1)*a(n-2) + (n-3)*(n-2)*(n-1)*a(n-3).
%F A294189 a(n) ~ 2^(1/3) * 3^(-1/2) * exp(-4/3 + 2^(1/3)*n^(1/3) + 3*2^(-1/3)*n^(2/3) - n) * n^(n - 1/6) * (1 + 19/(27*2^(1/3)*n^(1/3)) - 11/(3645*2^(2/3)*n^(2/3))). (End)
%t A294189 nmax = 20; CoefficientList[Series[E^(2*(1/(1-x)^2 - 1)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Aug 28 2025 *)
%o A294189 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(2*(1/(1-x)^2-1))))
%Y A294189 Column k=2 of A294188.
%Y A294189 Cf. A136658.
%K A294189 nonn,changed
%O A294189 0,2
%A A294189 _Seiichi Manyama_, Oct 24 2017