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 A370477 #17 Mar 31 2024 08:45:50
%S A370477 1,2,7,24,83,290,1023,3640,13052,47124,171190,625328,2295561,8464690,
%T A370477 31339455,116458200,434217000,1623971580,6090823890,22903571280,
%U A370477 86332453350,326145976884,1234662753126,4682968975664,17794062340008,67726620644200
%N A370477 G.f. satisfies A(x) = ( 1 + x * (A(x)^(1/2) / (1-x))^(3/2) )^2.
%F A370477 G.f.: B(x)^2 where B(x) is the g.f. of A071724.
%F A370477 a(n) = 2 * Sum_{k=0..n} binomial(3*k/2+2,k) * binomial(n+k/2-1,n-k)/(3*k/2+2).
%o A370477 (PARI) my(N=30, x='x+O('x^N)); Vec((1+x*((1-sqrt(1-4*x))/(2*x))^3)^2)
%o A370477 (PARI) a(n, r=2, s=3/2, t=3/2, 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 A370477 Cf. A045623, A370479.
%Y A370477 Cf. A071724, A370478.
%K A370477 nonn
%O A370477 0,2
%A A370477 _Seiichi Manyama_, Mar 31 2024