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 A372004 #15 Apr 22 2024 12:20:05
%S A372004 1,3,3,0,9,0,-63,189,0,-1944,6399,0,-72009,245430,0,-2921832,10184130,
%T A372004 0,-125775585,445134690,0,-5641620192,20188568790,0,-260832419406,
%U A372004 941254831539,0,-12342425759136,44833549152825,0,-594857401230510,2172276845159733,0
%N A372004 G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)*(1 + x*A(x)) )^(1/3).
%F A372004 a(n) = (1/(n+1)) * Sum_{k=0..n} 9^k * binomial(n/3+1/3,k) * binomial(k,n-k).
%F A372004 a(3*n+2) = 0 for n > 0.
%F A372004 a(n) = 9^n*binomial((n+1)/3, n)*hypergeom([(1-n)/2, -n/2], [2*(2-n)/3], 4/9)/(n+1). - _Stefano Spezia_, Apr 18 2024
%F A372004 D-finite with recurrence n*(n-1)*(2*n-11)*a(n) -108*(n-5)*(n-3)^2*a(n-3) -135*(n-5)*(n-8)*(2*n-5)*a(n-6)=0. - _R. J. Mathar_, Apr 22 2024
%p A372004 A372004 := proc(n)
%p A372004 add(9^k*binomial((n+1)/3,k)*binomial(k,n-k),k=0..n)/(n+1) ;
%p A372004 end proc:
%p A372004 seq(A372004(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A372004 (PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+1/3, k)*binomial(k, n-k))/(n+1);
%Y A372004 Cf. A372005, A372006.
%K A372004 sign
%O A372004 0,2
%A A372004 _Seiichi Manyama_, Apr 15 2024