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 A372125 #16 Nov 30 2024 08:50:01
%S A372125 1,1,4,13,60,256,1252,5979,30360,153626,801632,4197284,22355788,
%T A372125 119695396,647666544,3522773337,19298660772,106213538104,587632185580,
%U A372125 3264011196578,18203515158400,101862717712340,571859834176800,3219573318768300,18175140989890716
%N A372125 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)*(1 + 4*x*A(x))^(1/2) ).
%H A372125 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A372125 a(n) = (1/(n+1)) * Sum_{k=0..n} 4^(n-k) * binomial(n+k,k) * binomial(k/2,n-k).
%F A372125 From _Seiichi Manyama_, Nov 30 2024: (Start)
%F A372125 G.f.: exp( Sum_{k>=1} A378554(k) * x^k/k ).
%F A372125 a(n) = (1/(n+1)) * [x^n] 1/(1 - x*(1 + 4*x)^(1/2))^(n+1).
%F A372125 G.f.: (1/x) * Series_Reversion( x*(1 - x*(1 + 4*x)^(1/2)) ). (End)
%o A372125 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k, k)*binomial(k/2, n-k))/(n+1);
%Y A372125 Cf. A001002, A372126.
%Y A372125 Cf. A372012, A378554.
%K A372125 nonn
%O A372125 0,3
%A A372125 _Seiichi Manyama_, Apr 20 2024