A372016 - OEIS

A372016

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

%I #6 Apr 16 2024 10:23:07

%S 1,2,0,6,-2,38,-32,314,-436,3014,-5732,31954,-74934,363642,-983868,

%T 4360230,-13021586,54374950,-173933428,698713298,-2345075002,

%U 9189017010,-31903354068,123070336590,-437701811100,1672475509274,-6052049207112,22998585552814

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

%F 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 (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 Cf. A372002.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 15 2024