A060027 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 8.

1, 0, 1, 1, 2, 2, 4, 4, 6, 6, 9, 9, 13, 12, 16, 15, 18, 15, 18, 12, 12, 2, -3, -20, -31, -59, -81, -122, -160, -222, -280, -369, -457, -581, -708, -878, -1055, -1286, -1528, -1833, -2158, -2559, -2985, -3504, -4059, -4721, -5433, -6271, -7172, -8224, -9355, -10660, -12067

Offset: 0

Author

N. J. A. Sloane, Mar 17 2001

Keywords

• sign
• easy

Comments

Difference of the number of partitions of n+7 into 7 parts and the number of partitions of n+7 into 8 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, -1, 0, 1, 2, 1, 0, 1, -1, -1, -2, -1, -1, 1, 0, 1, 2, 1, 0, -1, 0, -1, 0, -1, 0, 0, 1, 1, -1).

Crossrefs

Cf. A026813, A026814.

Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), this sequence (N=8), A060028 (N=9), A060029 (N=10).

Programs

Mathematica

With[{nn=8},CoefficientList[Series[(1-x-x^nn)/Times@@(1-x^Range[nn]),{x,0,60}],x]] (* Harvey P. Dale, May 15 2016 *)

Formula

a(n) = A026813(n+7) - A026814(n+7). - Wesley Ivan Hurt, Apr 16 2019