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 A364748 #23 Dec 05 2024 07:14:37
%S A364748 1,1,6,47,424,4159,43097,464197,5145475,58313310,672598269,7869856070,
%T A364748 93183973405,1114471042413,13443614108307,163372291277764,
%U A364748 1998239045199623,24580340878055298,303893356012560280,3774099648814193998,47061518776483143441
%N A364748 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5 / (1 - x*A(x)).
%H A364748 Seiichi Manyama, <a href="/A364748/b364748.txt">Table of n, a(n) for n = 0..890</a>
%F A364748 a(n) = (1/n) * Sum_{k=0..n-1} binomial(n,k) * binomial(5*n-4*k,n-1-k) for n > 0.
%F A364748 From _Seiichi Manyama_, Dec 05 2024: (Start)
%F A364748 G.f. A(x) satisfies A(x) = 1/(1 - x*A(x)^4/(1 - x*A(x))).
%F A364748 If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r). (End)
%o A364748 (PARI) a(n) = if(n==0, 1, sum(k=0, n-1, binomial(n, k)*binomial(5*n-4*k, n-1-k))/n);
%o A364748 (PARI) a(n, r=1, s=1, t=5, u=1) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r)); \\ _Seiichi Manyama_, Dec 05 2024
%Y A364748 Cf. A000108, A001003, A108447, A364747, A378691, A378692.
%Y A364748 Cf. A002295, A243667, A365192, A365193, A365194.
%K A364748 nonn
%O A364748 0,3
%A A364748 _Seiichi Manyama_, Aug 05 2023