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 A379023 #13 Dec 14 2024 07:10:28
%S A379023 1,6,57,653,8277,111780,1576671,22955298,342377304,5204438258,
%T A379023 80334470136,1255798641861,19840021268937,316286673287724,
%U A379023 5081503084814883,82193597974971157,1337397202150986387,21875767255039745856,359499909751084059372,5932767953991599086905
%N A379023 Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^3 ).
%H A379023 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379023 G.f. A(x) satisfies:
%F A379023 (1) A(x) = exp( Sum_{k>=1} A379025(k) * x^k/k ).
%F A379023 (2) A(x) = ( (1 + x*A(x)) * (1 + x*A(x)^(4/3)) )^3.
%F A379023 (3) A(x) = B(x)^3 where B(x) is the g.f. of A239107.
%F A379023 a(n) = (1/(n+1)) * [x^n] ( (1 + x)/(1 - x - x^2) )^(3*(n+1)).
%F A379023 a(n) = 3 * Sum_{k=0..n} binomial(3*n+k+3,k) * binomial(3*n+k+3,n-k)/(3*n+k+3) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(3*n+k+3,n-k).
%o A379023 (PARI) a(n) = 3*sum(k=0, n, binomial(3*n+k+3, k)*binomial(3*n+k+3, n-k)/(3*n+k+3));
%Y A379023 Cf. A007863, A379021, A379024.
%Y A379023 Cf. A239107, A379025.
%K A379023 nonn
%O A379023 0,2
%A A379023 _Seiichi Manyama_, Dec 14 2024