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%I A372016 #6 Apr 16 2024 10:23:07
%S A372016 1,2,0,6,-2,38,-32,314,-436,3014,-5732,31954,-74934,363642,-983868,
%T A372016 4360230,-13021586,54374950,-173933428,698713298,-2345075002,
%U A372016 9189017010,-31903354068,123070336590,-437701811100,1672475509274,-6052049207112,22998585552814
%N A372016 G.f. A(x) satisfies A(x) = ( 1 + 4*x/(1 - x*A(x)) )^(1/2).
%F A372016 a(n) = Sum_{k=0..n} 4^k * binomial(n/2-k/2+1/2,k) * binomial(n-1,n-k)/(n-k+1).
%o A372016 (PARI) a(n) = sum(k=0, n, 4^k*binomial(n/2-k/2+1/2, k)*binomial(n-1, n-k)/(n-k+1));
%Y A372016 Cf. A372002.
%K A372016 sign
%O A372016 0,2
%A A372016 _Seiichi Manyama_, Apr 15 2024

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