A376728 Expansion of (1 + x^4 - x^5)/((1 + x^4 - x^5)^2 - 4*x^4).

1, 0, 0, 0, 3, 1, 0, 0, 5, 10, 1, 0, 7, 35, 21, 1, 9, 84, 126, 36, 12, 165, 462, 330, 68, 287, 1287, 1716, 730, 533, 3004, 6435, 5022, 2045, 6293, 19449, 24329, 13345, 14008, 50524, 92400, 76912, 47481, 120156, 294124, 354488, 237139, 299421, 823200, 1354588

Offset: 0

Author

Seiichi Manyama, Oct 03 2024

Keywords

• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,2,0,0,-1,2,-1).

Crossrefs

Cf. A099511, A376726, A376727.

Cf. A376725, A376731.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec((1+x^4-x^5)/((1+x^4-x^5)^2-4*x^4))

PARI

a(n) = sum(k=0, n\4, binomial(2*k+1, 2*n-8*k+1));

Formula

a(n) = 2*a(n-4) + 2*a(n-5) - a(n-8) + 2*a(n-9) - a(n-10).

a(n) = Sum_{k=0..floor(n/4)} binomial(2*k+1,2*n-8*k+1).