A060029 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

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).

FORMULA

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

MATHEMATICA

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

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).

Sequence in context: A208963 A011142 A232047 * A100471 A266777 A248518

Adjacent sequences: A060026 A060027 A060028 * A060030 A060031 A060032

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Mar 17 2001

STATUS

approved

Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.

Pfad - The Proxy pFad of © 2024 Garber Painting. All rights reserved.