A060029 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 10.

1, 0, 1, 1, 2, 2, 4, 4, 7, 8, 11, 12, 18, 19, 26, 29, 37, 40, 51, 53, 65, 68, 79, 80, 92, 87, 94, 84, 82, 58, 45, -1, -36, -109, -180, -297, -413, -594, -780, -1042, -1325, -1704, -2112, -2647, -3228, -3961, -4772, -5769, -6867, -8206, -9682, -11446, -13402, -15710

Offset: 0

Author

N. J. A. Sloane, Mar 17 2001

Keywords

• sign
• easy

Comments

Difference of the number of partitions of n+9 into 9 parts and the number of partitions of n+9 into 10 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, 0, -1, 1, 1, 1, 2, 0, 0, -1, -1, -1, -1, -3, 0, 0, 1, 1, 2, 2, 1, 1, 0, 0, -3, -1, -1, -1, -1, 0, 0, 2, 1, 1, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 1, 1, -1).

Crossrefs

Cf. A026815, A026816.

Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), A060028 (N=9), this sequence (N=10).

Programs

Mathematica

CoefficientList[Series[(1-x-x^10)/Times@@(1-x^Range[10]),{x,0,60}],x] (* Harvey P. Dale, May 15 2016 *)

Formula

a(n) = A026815(n+9) - A026816(n+9). - Wesley Ivan Hurt, Apr 16 2019