A060026 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 7.

1, 0, 1, 1, 2, 2, 4, 3, 5, 5, 7, 6, 9, 6, 8, 5, 5, -1, -2, -13, -18, -33, -45, -68, -86, -121, -151, -198, -244, -310, -373, -464, -553, -671, -793, -948, -1107, -1309, -1517, -1771, -2039, -2360, -2696, -3098, -3519, -4011, -4534, -5137, -5774, -6508, -7283, -8163, -9099, -10153, -11269

Offset

0,5

Comments

Difference of the number of partitions of n+6 into 6 parts and the number of partitions of n+6 into 7 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, -1, 0, 1, 1, 2, 0, 0, 0, -2, -1, -1, 0, 1, 1, 0, 1, 0, 0, -1, -1, 1).

Formula

a(n) = A026812(n+6) - A026813(n+6). - Wesley Ivan Hurt, Apr 16 2019

Mathematica

With[{nn=7}, CoefficientList[Series[(1-x-x^nn)/Times@@(1-x^Range[nn]), {x, 0, 60}], x]] (* Harvey P. Dale, May 15 2016 *)

Crossrefs

Cf. A026812, A026813.

Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), this sequence (N=7), A060027 (N=8), A060028 (N=9), A060029 (N=10).

Sequence in context: A007728 A262991 A077026 * A329437 A318632 A094051

Adjacent sequences: A060023 A060024 A060025 * A060027 A060028 A060029

Keyword

sign,easy

Author

N. J. A. Sloane, Mar 17 2001

Status

approved