A375292 Expansion of 1/sqrt((1 - x + x^3)^2 + 4*x^4).

1, 1, 1, 0, -3, -8, -14, -15, 1, 51, 146, 261, 286, -24, -1029, -2975, -5375, -5930, 591, 22014, 63886, 115947, 128183, -14595, -486466, -1413161, -2569868, -2840890, 361667, 10972167, 31861581, 57980426, 64018181, -8985428, -250991300, -727998021, -1324662165

Offset: 0

Author

Seiichi Manyama, Aug 10 2024

Keywords

• sign

Crossrefs

Cf. A375021, A375293.

Cf. A246840.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^3)^2+4*x^4))

PARI

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

Formula

n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - (2*n-3)*a(n-3) - 2*(n-2)*a(n-4) - (n-3)*a(n-6).

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