A375255 Expansion of 1/(1 - 2*x + 3*x^2 + 2*x^3 + x^4).

1, 2, 1, -6, -20, -26, 19, 162, 339, 180, -1000, -3380, -4459, 3042, 27221, 57614, 31940, -166446, -571161, -764478, 485479, 4573160, 9790000, 5654040, -27693719, -96502718, -131022359, 77196834, 768159900, 1663276734, 998702459, -4605941918, -16302704581

Offset: 0

Author

Seiichi Manyama, Aug 09 2024

Keywords

• sign

Links

• Index entries for linear recurrences with constant coefficients, signature (2,-3,-2,-1).

Crossrefs

Cf. A182890, A375273.

Cf. A375021, A375275.

Programs

PARI

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

PARI

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

Formula

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

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