A360315 - OEIS

%I #10 Feb 03 2023 08:18:19

%S 1,0,0,0,-2,-2,-2,-2,4,10,16,22,8,-26,-80,-154,-178,-82,204,750,1374,

%T 1642,868,-1886,-6886,-12802,-15784,-8538,17166,64554,122476,152602,

%U 86056,-157642,-616456,-1183666,-1493402,-878250,1468080

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

%F G.f.: 1 / sqrt(1+4*x^4/(1-x)).

%F n*a(n) = 2*(n-1)*a(n-1) - (n-2)*a(n-2) - 2*(2*n-4)*a(n-4) + 2*(2*n-7)*a(n-5).

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

%o (PARI) my(N=40, x='x+O('x^N)); Vec(1/sqrt(1+4*x^4/(1-x)))

%Y Cf. A360313, A360314.

%Y Cf. A360295, A360310.

%K sign

%O 0,5

%A _Seiichi Manyama_, Feb 03 2023