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 A349017 #26 Dec 04 2024 08:38:51
%S A349017 1,3,9,34,147,684,3341,16896,87702,464566,2501178,13646625,75289022,
%T A349017 419301351,2354121750,13309905653,75715795119,433063793430,
%U A349017 2488921730886,14366319150072,83246947358766,484082947060300,2823980738817453,16522429720210884,96928401308507100
%N A349017 G.f. A(x) satisfies A(x) = 1/(1 - x/(1 - x*A(x)))^3.
%H A349017 Seiichi Manyama, <a href="/A349017/b349017.txt">Table of n, a(n) for n = 0..1000</a>
%F A349017 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 A349017 a(n) ~ sqrt((1 - r*s)*(1 - r - r*s) / (1 - r*(s-1))) / (2*sqrt(Pi)*n^(3/2)* r^(n+1)), where r = 0.16019884639474132810520949540299923469792581229191347... and s = 2.80076422793129845097661115192234873280320027349745080... are real roots of the system of equations (-1 + r*s)^3/(-1 + r + r*s)^3 = s, (3*r^2*(-1 + r*s)^2)/(-1 + r + r*s)^4 = 1. - _Vaclav Kotesovec_, Nov 15 2021
%F A349017 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A300048. - _Seiichi Manyama_, Dec 04 2024
%o A349017 (PARI) a(n, s=1, t=3) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
%Y A349017 Cf. A262441, A349018.
%Y A349017 Cf. A300048.
%K A349017 nonn
%O A349017 0,2
%A A349017 _Seiichi Manyama_, Nov 06 2021