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A060024 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 5. 8
1, 0, 1, 1, 2, 1, 2, 1, 2, 0, 0, -3, -3, -8, -10, -16, -20, -29, -35, -47, -56, -72, -85, -105, -122, -148, -171, -202, -231, -270, -306, -353, -397, -453, -507, -573, -637, -715, -791, -881, -970, -1075, -1178, -1298, -1417, -1554, -1691, -1846, -2001, -2177, -2353, -2550, -2748, -2969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Difference of the number of partitions of n+4 into 4 parts and the number of partitions of n+4 into 5 parts. - Wesley Ivan Hurt, Apr 16 2019

LINKS

Colin Barker, 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,-1,-1,1,1,1,0,0,-1,-1,1).

FORMULA

a(0)=1, a(1)=0, a(2)=1, a(3)=1, a(4)=2, a(5)=1, a(6)=2, a(7)=1, a(8)=2, a(9)=0, a(10)=0, a(11)=-3, a(12)=-3, a(13)=-8, a(14)=-10, a(n) = a(n-1)+ a(n-2)-a(n-5)-a(n-6)-a(n-7)+a(n-8)+a(n-9)+a(n-10)-a(n-13)- a(n-14)+ a(n-15). - Harvey P. Dale, Dec 21 2015

a(n) = A026810(n+4) - A026811(n+4). - Wesley Ivan Hurt, Apr 16 2019

G.f.: (1 - x + x^2)*(1 - x^2 - x^3) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 17 2019

MATHEMATICA

CoefficientList[Series[(1-x-x^5)/(Times@@(1-x^Range[5])), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1}, {1, 0, 1, 1, 2, 1, 2, 1, 2, 0, 0, -3, -3, -8, -10}, 60] (* Harvey P. Dale, Dec 21 2015 *)

PROG

(PARI) Vec((1 - x + x^2)*(1 - x^2 - x^3) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)) + O(x^40)) \\ Colin Barker, Apr 17 2019

CROSSREFS

Cf. A026810, A026811.

Cf. For other values of N: A060022 (N=3), A060023 (N=4), this sequence (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), A060028 (N=9), A060029 (N=10).

Sequence in context: A323284 A010250 A268041 * A143668 A029445 A274920

Adjacent sequences:  A060021 A060022 A060023 * A060025 A060026 A060027

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Mar 17 2001

STATUS

approved

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Last modified June 12 10:58 EDT 2021. Contains 344947 sequences. (Running on oeis4.)