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 A378954 #11 Dec 12 2024 09:24:15
%S A378954 1,2,11,82,705,6584,64902,664608,7001006,75378082,825810304,
%T A378954 9176278104,103171720299,1171558985630,13416903518301,154784357304138,
%U A378954 1797153050309355,20984321920535966,246252819129444579,2902768234099178002,34355158795966317996,408086199665333171952
%N A378954 G.f. A(x) satisfies A(x) = ( 1 + x*A(x)^3/(1 + x*A(x)^2) )^2.
%F A378954 G.f. A(x) satisfies:
%F A378954 (1) A(x) = 1/( 1 - x*A(x)^(5/2)/(1 + x*A(x)^2) )^2.
%F A378954 (2) A(x) = 1 + x * A(x)^2 * (1 + A(x)^(3/2)).
%F A378954 (3) A(x) = B(x)^2 where B(x) is the g.f. of A364765.
%F A378954 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).
%o A378954 (PARI) a(n, r=2, s=-1, t=6, u=4) = 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 A378954 Cf. A364765, A378952.
%Y A378954 Cf. A262441, A366400, A370474.
%K A378954 nonn
%O A378954 0,2
%A A378954 _Seiichi Manyama_, Dec 12 2024