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 A372019 #12 Apr 22 2024 12:53:47
%S A372019 1,3,3,3,30,57,84,867,1893,3162,33132,76953,136812,1446204,3478764,
%T A372019 6420387,68260134,167946159,317782524,3392340186,8479140510,
%U A372019 16332164868,174873206424,442212416121,863222622780,9264327739716,23637757714788,46624054987452
%N A372019 G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)/(1 - x*A(x)) )^(1/3).
%F A372019 a(n) = (1/(n+1)) * Sum_{k=0..n} 9^k * binomial(n/3+1/3,k) * binomial(n-1,n-k).
%F A372019 D-finite with recurrence n*(n-1)*(n+1)*a(n) -8*(2*n-5)*(8*n^2-40*n+57)*a(n-3) +4096*(n-5)*(n-6)*(n-4)*a(n-6)=0. - _R. J. Mathar_, Apr 22 2024
%p A372019 A371019 := proc(n)
%p A372019 add(9^k*binomial((n+1)/3,k)*binomial(n-1,k-1),k=0..n) ;
%p A372019 %/(n+1) ;
%p A372019 end proc:
%p A372019 seq(A371019(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A372019 (PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+1/3, k)*binomial(n-1, n-k))/(n+1);
%Y A372019 Cf. A372018, A372020.
%Y A372019 Cf. A372004.
%K A372019 nonn
%O A372019 0,2
%A A372019 _Seiichi Manyama_, Apr 15 2024