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 A372109 #20 Nov 30 2024 08:49:54
%S A372109 1,2,12,90,758,6850,64904,636250,6399120,65661250,684665828,
%T A372109 7233956250,77278356246,833291781250,9057750917944,99144375156250,
%U A372109 1091857567068742,12089416175781250,134501879883249300,1502857085910156250,16857310306553767026
%N A372109 G.f. A(x) satisfies A(x) = ( (1 - x*A(x))/(1 - 5*x*A(x)) )^(1/2).
%H A372109 <a href="/index/Res#revert">Index entries for reversions of series</a>
%F A372109 a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+k-1/2,k) * binomial(n-1,n-k).
%F A372109 From _Seiichi Manyama_, Nov 30 2024: (Start)
%F A372109 G.f.: exp( Sum_{k>=1} A378551(k) * x^k/k ).
%F A372109 a(n) = (1/(n+1)) * [x^n] 1/(1 - 4*x/(1-x))^((n+1)/2).
%F A372109 G.f.: (1/x) * Series_Reversion( x*(1 - 4*x/(1-x))^(1/2) ). (End)
%o A372109 (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1/2, k)*binomial(n-1, n-k))/(n+1);
%Y A372109 Cf. A001003, A372110.
%Y A372109 Cf. A085362, A372018, A372090, A372104, A378551.
%K A372109 nonn
%O A372109 0,2
%A A372109 _Seiichi Manyama_, Apr 19 2024