A375293 Expansion of 1/sqrt((1 - x + x^4)^2 + 4*x^5).

1, 1, 1, 1, 0, -3, -8, -15, -23, -26, -12, 37, 144, 326, 564, 753, 633, -281, -2699, -7346, -14333, -21858, -24097, -8635, 45094, 162928, 362513, 620686, 813906, 633510, -495381, -3408175, -8939865, -17141831, -25663802, -27145201, -6079518, 62953931

Offset: 0

Author

Seiichi Manyama, Aug 10 2024

Keywords

• sign

Crossrefs

Cf. A375021, A375292.

Cf. A246883.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/sqrt((1-x+x^4)^2+4*x^5))

PARI

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

Formula

n*a(n) = (2*n-1)*a(n-1) - (n-1)*a(n-2) - 2*(n-2)*a(n-4) - (2*n-5)*a(n-5) - (n-4)*a(n-8).

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