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%I #9 Apr 19 2024 10:31:10
%S 1,2,12,90,758,6850,64904,636250,6399120,65661250,684665828,
%T 7233956250,77278356246,833291781250,9057750917944,99144375156250,
%U 1091857567068742,12089416175781250,134501879883249300,1502857085910156250,16857310306553767026
%N G.f. A(x) satisfies A(x) = ( (1 - x*A(x))/(1 - 5*x*A(x)) )^(1/2).
%F a(n) = (1/(n+1)) * Sum_{k=0..n} 4^k * binomial(n/2+k-1/2,k) * binomial(n-1,n-k).
%o (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2+k-1/2, k)*binomial(n-1, n-k))/(n+1);
%Y Cf. A372090.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Apr 19 2024
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