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