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 A373620 #15 Jun 11 2024 08:17:41
%S A373620 1,1,1,13,49,481,3841,38221,464353,5368609,82042561,1151767981,
%T A373620 20242097041,342921513793,6705416722369,133590317946541,
%U A373620 2880298682358721,65597610230669761,1556262483879791233,39569880403136366029,1030778206965403668721
%N A373620 Expansion of e.g.f. exp(x / (1 - x^2)^2).
%F A373620 a(n) = n! * Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1,k)/(n-2*k)!.
%F A373620 a(n) == 1 mod 12.
%F A373620 a(n) ~ 2^(-1/6) * 3^(-1/2) * exp(1/48 + 2^(-5/3)*n^(1/3) + 3*2^(-4/3)*n^(2/3) - n) * n^(n - 1/6). - _Vaclav Kotesovec_, Jun 11 2024
%F A373620 D-finite with recurrence a(n) -a(n-1) -3*(n-1)*(n-2)*a(n-2) -3*(n-1)*(n-2)*a(n-3) +3*(n-1)*(n-2)*(n-3)*(n-4)*a(n-4) -(n-1)*(n-2)*(n-3)*(n-4)*(n-5)*(n-6)*a(n-6)=0. - _R. J. Mathar_, Jun 11 2024
%p A373620 A373620 := proc(n)
%p A373620 add(binomial(2*n-3*k-1,k)/(n-2*k)!,k=0..floor(n/2)) ;
%p A373620 %*n! ;
%p A373620 end proc:
%p A373620 seq(A373620(n),n=0..80) ; # _R. J. Mathar_, Jun 11 2024
%o A373620 (PARI) a(n) = n!*sum(k=0, n\2, binomial(2*n-3*k-1, k)/(n-2*k)!);
%Y A373620 Cf. A012150, A088009, A373619.
%Y A373620 Cf. A082579, A373578.
%K A373620 nonn
%O A373620 0,4
%A A373620 _Seiichi Manyama_, Jun 11 2024