A376810 - OEIS

%I #8 Oct 05 2024 02:48:09

%S 1,2,6,24,94,378,1544,6380,26598,111658,471358,1998924,8509368,

%T 36341278,155634228,668116136,2874157222,12387209982,53475080494,

%U 231189987224,1000834283190,4337864724462,18821884379924,81748960355484,355383570351664,1546239230878154

%N Expansion of 1/sqrt(1 - 4*x/(1 - x^2)^2).

%F a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-3*k-1,k) * binomial(2*n-4*k,n-2*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x/(1-x^2)^2))

%o (PARI) a(n) = sum(k=0, n\2, binomial(2*n-3*k-1, k)*binomial(2*n-4*k, n-2*k));

%Y Cf. A110170, A376811.

%Y Cf. A349713.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Oct 04 2024