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 A382919 #12 Apr 09 2025 07:28:48
%S A382919 1,2,13,84,580,4216,31824,247168,1962800,15866016,130122304,
%T A382919 1080101760,9057113472,76610188544,652895283200,5600752756224,
%U A382919 48323092761344,419068973537792,3650909105378304,31937405800724480,280419948474447872,2470473454986891264
%N A382919 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x) / (1-x)^3 )^2.
%F A382919 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^(3/2) / (1-x)^3 )^2.
%F A382919 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).
%F A382919 G.f.: B(x)^2, where B(x) is the g.f. of A213282.
%o A382919 (PARI) a(n, r=2, s=3, t=3, u=0) = 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));
%Y A382919 Cf. A360100, A382921.
%Y A382919 Cf. A213282, A382616.
%K A382919 nonn
%O A382919 0,2
%A A382919 _Seiichi Manyama_, Apr 08 2025