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 A373519 #23 Sep 03 2025 10:11:46
%S A373519 1,1,1,1,1,31,181,631,1681,60481,687961,4379761,19982161,802740511,
%T A373519 13848694861,131732390791,873339798241,38385869907841,894783905472241,
%U A373519 11506538747852641,101612306808695521,4824806928717603871,142148609212891008421
%N A373519 Expansion of e.g.f. exp(x/(1 - x^4)^(1/4)).
%H A373519 Vaclav Kotesovec, <a href="/A373519/a373519.jpg">Graph - the asymptotic ratio (20000 terms)</a>
%F A373519 a(n) = n! * Sum_{k=0..floor(n/4)} binomial(n/4-1,k)/(n-4*k)!.
%F A373519 a(n) == 1 mod 30.
%F A373519 From _Vaclav Kotesovec_, Sep 03 2025: (Start)
%F A373519 a(n) = (5*n^4 - 80*n^3 + 505*n^2 - 1480*n + 1681)*a(n-4) - 5*(n-8)*(n-7)*(n-6)^2*(n-5)*(n-4)*(2*n^2 - 24*n + 85)*a(n-8) + 5*(n-12)*(n-11)*(n-10)*(n-9)*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*(2*n^2 - 32*n + 135)*a(n-12) - 5*(n-16)*(n-15)*(n-14)*(n-13)*(n-12)^2*(n-11)*(n-10)^2*(n-9)*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*a(n-16) + (n-20)*(n-19)*(n-18)*(n-17)*(n-16)^2*(n-15)*(n-14)*(n-13)*(n-12)^2*(n-11)*(n-10)*(n-9)*(n-8)^2*(n-7)*(n-6)*(n-5)*(n-4)*a(n-20).
%F A373519 a(n) ~ 5^(-1/2) * exp(5*n^(1/5)/4 - n) * n^(n - 2/5).
%F A373519 (End)
%t A373519 nmax = 25; CoefficientList[Series[E^(x/(1 - x^4)^(1/4)), {x, 0, nmax}], x] * Range[0, nmax]! (* _Vaclav Kotesovec_, Sep 03 2025 *)
%o A373519 (PARI) a(n) = n!*sum(k=0, n\4, binomial(n/4-1, k)/(n-4*k)!);
%Y A373519 Cf. A293507, A373520, A373521.
%Y A373519 Cf. A373524.
%Y A373519 Cf. A000262, A012150, A373517.
%K A373519 nonn,changed
%O A373519 0,6
%A A373519 _Seiichi Manyama_, Jun 08 2024