A306942 Expansion of 1/((1 - x)^9 + x^9).

1, 9, 45, 165, 495, 1287, 3003, 6435, 12870, 24309, 43740, 75411, 124830, 197505, 293436, 389367, 389367, 0, -1562274, -6216183, -18365697, -47600136, -113879520, -257123889, -554298228, -1148646906, -2297293812, -4443424371, -8313049440, -15011769204

Offset: 0

Author

Seiichi Manyama, Mar 17 2019

Keywords

• sign
• 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).

Crossrefs

Column 9 of A306914.

Cf. A306939.

Programs

Mathematica

CoefficientList[Series[1/((1-x)^9+x^9),{x,0,30}],x] (* Harvey P. Dale, Sep 25 2019 *)

PARI

{a(n) = sum(k=0, n\9, (-1)^k*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)} (-1)^k*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) for n > 7.