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 A379021 #12 Dec 14 2024 07:10:40
%S A379021 1,4,26,206,1813,17032,167287,1697044,17643322,186997570,2012973499,
%T A379021 21948003052,241883091289,2690117648372,30153678822007,
%U A379021 340305271736134,3863616751855069,44097785533620550,505692279260755753,5823592506326814874,67320958983831426221
%N A379021 Expansion of (1/x) * Series_Reversion( x * ((1 - x - x^2)/(1 + x))^2 ).
%H A379021 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A379021 G.f. A(x) satisfies:
%F A379021 (1) A(x) = exp( Sum_{k>=1} A379022(k) * x^k/k ).
%F A379021 (2) A(x) = ( (1 + x*A(x)) * (1 + x*A(x)^(3/2)) )^2.
%F A379021 (3) A(x) = B(x)^2 where B(x) is the g.f. of A215654.
%F A379021 a(n) = (1/(n+1)) * [x^n] ( (1 + x)/(1 - x - x^2) )^(2*(n+1)).
%F A379021 a(n) = 2 * Sum_{k=0..n} binomial(2*n+k+2,k) * binomial(2*n+k+2,n-k)/(2*n+k+2) = (1/(n+1)) * Sum_{k=0..n} binomial(2*n+k+1,k) * binomial(2*n+k+2,n-k).
%o A379021 (PARI) a(n) = 2*sum(k=0, n, binomial(2*n+k+2, k)*binomial(2*n+k+2, n-k)/(2*n+k+2));
%Y A379021 Cf. A007863, A379023, A379024.
%Y A379021 Cf. A215654, A379022.
%K A379021 nonn
%O A379021 0,2
%A A379021 _Seiichi Manyama_, Dec 14 2024