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 A349018 #22 Dec 04 2024 08:39:40
%S A349018 1,4,14,60,297,1584,8868,51412,305964,1858308,11472152,71774548,
%T A349018 454080514,2899959640,18670920458,121056521536,789733186076,
%U A349018 5180002637472,34141018474400,225995779077324,1501809350268648,10015202238242356,67003372168525774
%N A349018 G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)))^4.
%H A349018 Seiichi Manyama, <a href="/A349018/b349018.txt">Table of n, a(n) for n = 0..1000</a>
%F A349018 If g.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
%F A349018 a(n) ~ sqrt((1 - r*s)*(1 - r - r*s) / (2 - r*(2*s - 3))) / (sqrt(2*Pi) * n^(3/2) * r^(n+1)), where r = 0.13968480593491705709394976139265608086009606657813769... and s = 3.10146641162846907900664383717504887133026560522911567... are real roots of the system of equations (-1 + r*s)^4/(-1 + r + r*s)^4 = s, (4*r^2*(-1 + r*s)^3)/(-1 + r + r*s)^5 = 1. - _Vaclav Kotesovec_, Nov 15 2021
%F A349018 G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A364723. - _Seiichi Manyama_, Dec 04 2024
%o A349018 (PARI) a(n, s=1, t=4) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
%Y A349018 Cf. A262441, A349017.
%Y A349018 Cf. A364723.
%K A349018 nonn
%O A349018 0,2
%A A349018 _Seiichi Manyama_, Nov 06 2021