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 A372138 #7 Apr 20 2024 10:23:23
%S A372138 1,1,5,24,149,945,6464,45360,328661,2426971,18244053,138988092,
%T A372138 1071271988,8336754044,65421283160,517081111568,4112772482949,
%U A372138 32894217211791,264391091936095,2134466592084000,17300375657257629,140728012021470193,1148477345709237844
%N A372138 G.f. A(x) satisfies A(x) = 1/( 1 - x*A(x)^2*(1 + 4*x*A(x))^(1/2) ).
%F A372138 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+2*k,k) * binomial(k/2,n-k)/(n+k+1).
%o A372138 (PARI) a(n) = sum(k=0, n, 4^(n-k)*binomial(n+2*k, k)*binomial(k/2, n-k)/(n+k+1));
%Y A372138 Cf. A372136.
%K A372138 nonn
%O A372138 0,3
%A A372138 _Seiichi Manyama_, Apr 20 2024