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 A370474 #21 Dec 12 2024 09:24:11
%S A370474 1,2,9,54,372,2778,21873,178786,1502649,12904524,112741664,998871030,
%T A370474 8953443276,81047485148,739846170864,6803054508702,62954736555836,
%U A370474 585850907166084,5479077065774682,51470699845616004,485456696541512442,4595280949098247422
%N A370474 G.f. A(x) satisfies A(x) = 1 + x * A(x)^(3/2) * (1 + A(x)^(3/2)).
%F A370474 a(n) = Sum{k=0..n} binomial(n,k) * binomial(3*n/2+3*k/2+1,n)/(3*n/2+3*k/2+1).
%F A370474 From _Seiichi Manyama_, Dec 12 2024: (Start)
%F A370474 G.f. A(x) satisfies:
%F A370474 (1) A(x) = ( 1 + x*A(x)^(5/2)/(1 + x*A(x)^(3/2)) )^2.
%F A370474 (2) A(x) = 1/( 1 - x*A(x)^2/(1 + x*A(x)^(3/2)) )^2.
%F A370474 (3) A(x) = B(x)^2 where B(x) is the g.f. of A271469.
%F A370474 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)
%o A370474 (PARI) a(n) = sum(k=0, n, binomial(n, k)*binomial(3*n/2+3*k/2+1, n)/(3*n/2+3*k/2+1));
%o A370474 (PARI) a(n, r=2, s=-1, t=5, u=3) = 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 A370474 Cf. A006013, A370475.
%Y A370474 Cf. A262441, A366400.
%Y A370474 Cf. A271469.
%K A370474 nonn
%O A370474 0,2
%A A370474 _Seiichi Manyama_, Mar 31 2024