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 A379522 #14 Dec 25 2024 09:17:16
%S A379522 1,9,114,1683,27111,462060,8192078,149541975,2791795695,53056724409,
%T A379522 1023021616920,19963667407572,393536736830724,7824888965728584,
%U A379522 156750391932619254,3160558799674447167,64092227061832430895,1306327265854324847595,26746550927141536784370
%N A379522 Expansion of (1/x) * Series_Reversion( x / ( (1+x)^3 * (1+2*x)^3 ) ).
%H A379522 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379522 a(n) = (1/(n+1)) * Sum_{k=0..n} 2^k * binomial(3*(n+1),k) * binomial(3*(n+1),n-k).
%F A379522 a(n) = (1/(n+1)) * [x^n] ( (1+x) * (1+2*x) )^(3*(n+1)).
%o A379522 (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3*(1+2*x)^3))/x)
%o A379522 (PARI) a(n) = sum(k=0, n, 2^k*binomial(3*(n+1), k)*binomial(3*(n+1), n-k))/(n+1);
%Y A379522 Cf. A243659, A379521.
%K A379522 nonn
%O A379522 0,2
%A A379522 _Seiichi Manyama_, Dec 24 2024