A369808 Expansion of 1/(1 - x^5/(1-x)^7).

1, 0, 0, 0, 0, 1, 7, 28, 84, 210, 463, 938, 1821, 3563, 7385, 16577, 39529, 96315, 232393, 546806, 1251461, 2801015, 6189683, 13647361, 30281870, 67918782, 153939843, 351309676, 803438125, 1834160110, 4170751775, 9443922772, 21316094357, 48041401423, 108291578580

Offset: 0

Author

Seiichi Manyama, Feb 01 2024

Keywords

• nonn

Comments

Number of compositions of 7*n-5 into parts 5 and 7.

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,22,-7,1).

Crossrefs

Cf. A099253, A369805, A369806, A369807, A369809.

Cf. A369816.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(1/(1-x^5/(1-x)^7))

PARI

a(n) = sum(k=0, n\5, binomial(n-1+2*k, n-5*k));

Formula

a(n) = A369816(7*n-5) for n > 0.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 22*a(n-5) - 7*a(n-6) + a(n-7) for n > 7.

a(n) = Sum_{k=0..floor(n/5)} binomial(n-1+2*k,n-5*k).