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 A060025 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 6. 8
 1, 0, 1, 1, 2, 2, 3, 2, 4, 3, 4, 2, 3, -1, -1, -6, -9, -17, -22, -35, -43, -61, -76, -100, -121, -155, -185, -229, -271, -328, -383, -458, -529, -622, -715, -830, -946, -1090, -1233, -1407, -1584, -1794, -2008, -2261, -2517, -2816, -3124, -3476, -3838, -4253, -4677, -5159, -5656, -6213 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Difference of the number of partitions of n+5 into 5 parts and the number of partitions of n+5 into 6 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 linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1). FORMULA a(n) = A026811(n+5) - A026812(n+5). - Wesley Ivan Hurt, Apr 16 2019 G.f.: (1 - x - x^6) / ((1 - x)^6*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, Apr 17 2019 MATHEMATICA With[{nn=6}, CoefficientList[Series[(1-x-x^nn)/Times@@(1-x^Range[nn]), {x, 0, 60}], x]] (* Harvey P. Dale, May 15 2016 *) PROG (PARI) Vec((1 - x - x^6) / ((1 - x)^6*(1 + x)^3*(1 - x + x^2)*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Apr 17 2019 (MAGMA) m:=6; R:=PowerSeriesRing(Integers(), 60); Coefficients(R!( (1-x-x^m)/( (&*[1-x^j: j in [1..m]]) ) )); // G. C. Greubel, Apr 17 2019 (Sage) m=6; ((1-x-x^m)/( product(1-x^j for j in (1..m)) )).series(x, 60).coefficients(x, sparse=False) # G. C. Greubel, Apr 17 2019 CROSSREFS Cf. A026811, A026812. Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), this sequence (N=6), A060026 (N=7), A060027 (N=8), A060028 (N=9), A060029 (N=10). Sequence in context: A334857 A331614 A343541 * A067399 A106737 A323164 Adjacent sequences:  A060022 A060023 A060024 * A060026 A060027 A060028 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.)