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 A379521 #17 Dec 25 2024 09:17:08
%S A379521 1,7,68,767,9425,122436,1653776,22992655,326863667,4729547023,
%T A379521 69424933968,1031309398852,15474833826028,234201961398776,
%U A379521 3570887895432504,54799089019823407,845757173849239415,13119400228929684885,204429551432900950068,3198423097762769254279,50225078058311068601425
%N A379521 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^2 ) ).
%H A379521 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379521 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(2*(n+1),k) * binomial(3*(n+1),n-k).
%F A379521 a(n) = (1/(n+1)) * [x^n] ( (1+x)^3 * (1+2*x)^2 )^(n+1).
%o A379521 (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1+2*x)^2))/x)
%o A379521 (PARI) a(n) = sum(k=0, n, 2^k*binomial(2*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);
%Y A379521 Cf. A243659, A379522.
%K A379521 nonn
%O A379521 0,2
%A A379521 _Seiichi Manyama_, Dec 24 2024