A371612 - OEIS

%I #11 Mar 30 2024 02:36:44

%S 1,2,3,12,49,218,1037,5106,25909,134410,709691,3801498,20606654,

%T 112828202,623087675,3466539248,19411070496,109313442562,618713495451,

%U 3517737628368,20081523836403,115058714898196,661432784830204,3813891082337178,22052422636145522

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

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

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

%Y Cf. A365118, A371613.

%Y Cf. A364743, A371607.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 29 2024