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 A382894 #9 Apr 08 2025 08:47:09
%S A382894 1,2,13,78,520,3664,26859,202808,1566693,12323982,98381841,795023284,
%T A382894 6490951398,53462144788,443683640945,3706539244272,31144893093298,
%U A382894 263052053436600,2231992880546400,19016760502183968,162629329186013523,1395500273826639540
%N A382894 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^3 * A(x) )^2.
%F A382894 G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^3 * A(x)^(3/2) )^2.
%F A382894 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(s*k,n-k)/(t*k+u*(n-k)+r).
%F A382894 G.f.: B(x)^2, where B(x) is the g.f. of A366200.
%o A382894 (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(s*k, n-k)/(t*k+u*(n-k)+r));
%Y A382894 Cf. A360076, A382892.
%Y A382894 Cf. A366200, A382613.
%K A382894 nonn
%O A382894 0,2
%A A382894 _Seiichi Manyama_, Apr 08 2025