A060028 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 9.

1, 0, 1, 1, 2, 2, 4, 4, 7, 7, 10, 11, 16, 16, 22, 23, 29, 29, 36, 34, 41, 37, 40, 32, 32, 14, 6, -22, -44, -90, -130, -203, -270, -378, -487, -642, -803, -1027, -1260, -1568, -1899, -2320, -2774, -3342, -3955, -4706, -5526, -6507, -7579, -8854, -10243, -11872, -13656

Offset: 0

Author

N. J. A. Sloane, Mar 17 2001

Keywords

• sign
• easy

Comments

Difference of the number of partitions of n+8 into 8 parts and the number of partitions of n+8 into 9 parts. - Wesley Ivan Hurt, Apr 16 2019

Links

• Ray Chandler, Table of n, a(n) for n = 0..1000
• P. A. MacMahon, Perpetual reciprocants, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.
• Index entries for sequences related to partitions
• Index entries for linear recurrences with constant coefficients, signature (1, 1, 0, 0, -1, 0, -1, 0, 0, -1, 0, 2, 1, 1, 1, 0, -1, -1, -1, -2, -1, -1, 1, 1, 2, 1, 1, 1, 0, -1, -1, -1, -2, 0, 1, 0, 0, 1, 0, 1, 0, 0, -1, -1, 1).

Crossrefs

Cf. A026814, A026815.

Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), this sequence (N=9), A060029 (N=10).

Programs

Mathematica

With[{den=Times@@Table[(1-x^n),{n,9}]},CoefficientList[Series[(1-x-x^9)/ den,{x,0,60}],x]] (* Harvey P. Dale, May 22 2012 *)

Formula

a(n) = A026814(n+8) - A026815(n+8). - Wesley Ivan Hurt, Apr 16 2019