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 A373520 #17 Sep 03 2025 10:50:46
%S A373520 1,1,1,1,1,61,361,1261,3361,143641,1829521,12501721,59922721,
%T A373520 2173048021,44315751481,478799701381,3492321094081,116722067432881,
%U A373520 3290135175240481,50242015215929521,508061488330088641,16418736123292904941,585427887134915295241
%N A373520 Expansion of e.g.f. exp(x/(1 - x^4)^(1/2)).
%F A373520 a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n/2-k-1,k)/(n-4*k)!.
%F A373520 a(n) == 1 mod 60.
%F A373520 From _Vaclav Kotesovec_, Sep 03 2025: (Start)
%F A373520 Recurrence: (n-8)*a(n) = (n-8)*a(n-2) + 3*(n-4)*(n-3)*(n-2)*(n^2 - 11*n + 20)*a(n-4) + 2*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*a(n-6) - 3*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)*(n-3)*(n-2)*(n^2 - 13*n + 32)*a(n-8) + (n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)^2*(n-3)*(n-2)*a(n-10) + (n-12)*(n-11)^2*(n-10)*(n-9)*(n-8)*(n-7)*(n-6)*(n-5)*(n-4)^2*(n-3)*(n-2)*a(n-12).
%F A373520 a(n) ~ 2^(-1/6) * 3^(-1/2) * exp(3*2^(-4/3)*n^(1/3) - n) * n^(n - 1/3).
%F A373520 (End)
%t A373520 nmax = 25; CoefficientList[Series[E^(x/(1 - x^4)^(1/2)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 03 2025 *)
%o A373520 (PARI) a(n) = n!*sum(k=0, n\4, binomial(n/2-k-1, k)/(n-4*k)!);
%Y A373520 Cf. A293507, A373519, A373521.
%Y A373520 Cf. A373525.
%K A373520 nonn,changed
%O A373520 0,6
%A A373520 _Seiichi Manyama_, Jun 08 2024