A306939 Expansion of 1/((1 - x)^9 - x^9).

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24311, 43776, 75753, 127110, 209475, 346104, 591261, 1081575, 2163150, 4686826, 10656387, 24582663, 56191734, 125640180, 273241161, 577147212, 1184959314, 2369918628, 4631710931, 8881943832, 16798969548, 31537530456

Offset: 0

Author

Seiichi Manyama, Mar 17 2019

Keywords

• nonn
• easy

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..3000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,2).

Crossrefs

Column 9 of A306915.

Cf. A306860.

Programs

Mathematica

CoefficientList[Series[1/((1 - x)^9 - x^9), {x, 0, 30}], x] (* Amiram Eldar, May 25 2021 *)

PARI

{a(n) = sum(k=0, n\9, binomial(n+8, 9*k+8))}

PARI

N=66; x='x+O('x^N); Vec(1/((1-x)^9-x^9))

Formula

a(n) = Sum_{k=0..floor(n/9)} binomial(n+8,9*k+8).

a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + 2*a(n-9) for n > 8.