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 A371394 #11 Mar 21 2024 09:20:11
%S A371394 1,10,137,2174,37562,686004,13027065,254641398,5089756958,
%T A371394 103552330700,2137385941418,44647634773420,942085264713556,
%U A371394 20050276273007080,429913404536172633,9278142975370425510,201383222768034837750,4393265621094818733660
%N A371394 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+3*x)^3 ).
%H A371394 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A371394 a(n) = (1/(n+1)) * Sum_{k=0..n} 3^k * binomial(3*(n+1),k) * binomial(2*n-k,n-k).
%o A371394 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+3*x)^3)/x)
%o A371394 (PARI) a(n) = sum(k=0, n, 3^k*binomial(3*(n+1), k)*binomial(2*n-k, n-k))/(n+1);
%Y A371394 Cf. A082298, A371393.
%Y A371394 Cf. A365816.
%K A371394 nonn
%O A371394 0,2
%A A371394 _Seiichi Manyama_, Mar 21 2024