A372012 - OEIS

%I #13 Apr 19 2024 10:31:21

%S 1,-1,3,-5,17,-31,119,-211,937,-1483,8015,-10187,73369,-62193,713907,

%T -234857,7358657,1881661,80117735,69295469,917837521,1334044075,

%U 11006114883,21830065899,137275956089,333858963899,1769128762419,4940496514271,23409778504937

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

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

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

%Y Cf. A166587, A362154, A372013.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 19 2024