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 A371516 #14 Mar 27 2024 08:54:08
%S A371516 1,3,15,82,477,2901,18235,117555,773085,5166478,34987170,239570655,
%T A371516 1655933060,11538839130,80971109712,571702698185,4058556404958,
%U A371516 28951715755830,207424064434502,1491898838023884,10768487956456506,77977009814421534,566310026687320290
%N A371516 G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1-x))^3.
%F A371516 a(n) = 3 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+2,k)/(2*k+3) = Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+3,k)/(k+1).
%F A371516 G.f.: A(x) = B(x)^3 where B(x) is the g.f. of A307678.
%o A371516 (PARI) a(n) = 3*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+2, k)/(2*k+3));
%Y A371516 Cf. A045868, A371517, A371520, A371521.
%Y A371516 Cf. A270386, A307678.
%Y A371516 Cf. A371483.
%K A371516 nonn
%O A371516 0,2
%A A371516 _Seiichi Manyama_, Mar 26 2024