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G.f. A(x) satisfies A(x) = ( 1 + 4*x/(1 - x*A(x))^2 )^(1/2).
1

%I #7 Apr 16 2024 10:26:45

%S 1,2,2,10,18,90,210,1010,2754,12754,38626,173434,566034,2481578,

%T 8556722,36848994,132406274,562781730,2086628034,8786281322,

%U 33372861074,139609461370,540319600530,2250413871698,8838703576002,36709888093938,145870057771938

%N G.f. A(x) satisfies A(x) = ( 1 + 4*x/(1 - x*A(x))^2 )^(1/2).

%F a(n) = Sum_{k=0..n} 4^k * binomial(n/2-k/2+1/2,k) * binomial(n+k-1,n-k)/(n-k+1).

%o (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2-k/2+1/2, k)*binomial(n+k-1, n-k)/(n-k+1));

%Y Cf. A372022.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 16 2024