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 A294213 #22 Oct 19 2023 12:53:38
%S A294213 1,1,5,25,193,1601,16741,190345,2509025,35825473,569012581,9716400761,
%T A294213 180303804385,3569527588225,75681964322693,1700163418683241,
%U A294213 40499757023856961,1016190431274596225,26843084299482509125,743180975111364212953
%N A294213 E.g.f.: exp(1/((1-x)*(1-x^2)) - 1).
%H A294213 Seiichi Manyama, <a href="/A294213/b294213.txt">Table of n, a(n) for n = 0..435</a>
%F A294213 a(n) ~ exp(-61/96 + 3*n^(1/3)/4 + 3*n^(2/3)/2 - n) * n^(n - 1/6) / sqrt(3) * (1 + 25/(64*n^(1/3))). - _Vaclav Kotesovec_, Oct 26 2017
%F A294213 a(n) = n*a(n-1) + (n-1)*(2*n - 1)*a(n-2) - 2*(n-3)*(n-2)*(n-1)*a(n-3) - (n-4)*(n-3)*(n-2)*(n-1)*a(n-4) + (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*a(n-5). - _Vaclav Kotesovec_, Dec 02 2021
%F A294213 From _Peter Bala_, Oct 17 2023: (Start)
%F A294213 a(n+k) == a(n) (mod k) for all n and k >= 1. Hence for each k, the sequence a(n) taken modulo k is a periodic sequence and the period divides k. Cf. A047974.
%F A294213 a(5*n + 2) == a(5*n + 3) == 0 (mod 5);
%F A294213 a(25*n + 3) == a(25*n + 8) == a(25*n + 13) == a(25*n + 17) == a(25*n + 18) == a(25*n + 23) == 0 (mod 5^2);
%F A294213 a(125*n + 18) == a(125*n + 67) == a(125*n + 93) == a(125*n + 118) == 0 (mod 5^3). (End)
%t A294213 nmax = 20; CoefficientList[Series[E^(1/((1-x)*(1-x^2)) - 1), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Oct 26 2017 *)
%o A294213 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(1/((1-x)*(1-x^2))-1)))
%Y A294213 Column k=2 of A294212.
%K A294213 nonn,easy
%O A294213 0,3
%A A294213 _Seiichi Manyama_, Oct 25 2017