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 A366400 #25 Feb 03 2025 09:49:30
%S A366400 1,2,7,32,167,942,5593,34438,217888,1407938,9252168,61641846,
%T A366400 415412036,2826736736,19395080061,134034296976,932110471089,
%U A366400 6518146460274,45805553781349,323313555424924,2291130483593189,16294149468133930,116259325138469680
%N A366400 G.f. A(x) satisfies A(x) = (1 + x * A(x)^(5/2)) / (1 - x).
%F A366400 a(n) = Sum_{k=0..n} binomial(n+3*k/2,n-k) * binomial(5*k/2,k) / (3*k/2+1).
%F A366400 From _Seiichi Manyama_, Dec 12 2024: (Start)
%F A366400 G.f. A(x) satisfies:
%F A366400 (1) A(x) = ( 1 + x*A(x)^2/(1 + x*A(x)) )^2.
%F A366400 (2) A(x) = 1/( 1 - x*A(x)^(3/2)/(1 + x*A(x)) )^2.
%F A366400 (3) A(x) = 1 + x * A(x) * (1 + A(x)^(3/2)).
%F A366400 (4) A(x) = B(x)^2 where B(x) is the g.f. of A219537.
%F A366400 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). (End)
%F A366400 G.f.: Sum_{k>=0} binomial(5*k/2, k)*x^k/((3*k/2 + 1)*(1 - x)^(5*k/2 + 1)). - _Miles Wilson_, Feb 02 2025
%o A366400 (PARI) a(n) = sum(k=0, n, binomial(n+3*k/2, n-k)*binomial(5*k/2, k)/(3*k/2+1));
%o A366400 (PARI) a(n, r=2, s=-1, t=4, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r)); \\ _Seiichi Manyama_, Dec 12 2024
%Y A366400 Cf. A349311, A366401, A366402, A366403, A366404, A366405, A366406, A366407.
%Y A366400 Cf. A262441, A370474.
%Y A366400 Cf. A219537, A378890.
%K A366400 nonn
%O A366400 0,2
%A A366400 _Seiichi Manyama_, Oct 09 2023