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A060028 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 9. 8

%I

%S 1,0,1,1,2,2,4,4,7,7,10,11,16,16,22,23,29,29,36,34,41,37,40,32,32,14,

%T 6,-22,-44,-90,-130,-203,-270,-378,-487,-642,-803,-1027,-1260,-1568,

%U -1899,-2320,-2774,-3342,-3955,-4706,-5526,-6507,-7579,-8854,-10243,-11872,-13656

%N Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 9.

%C Difference of the number of partitions of n+8 into 8 parts and the number of partitions of n+8 into 9 parts. - _Wesley Ivan Hurt_, Apr 16 2019

%H P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s1-17.1.139">Perpetual reciprocants</a>, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F a(n) = A026814(n+8) - A026815(n+8). - _Wesley Ivan Hurt_, Apr 16 2019

%t With[{den=Times@@Table[(1-x^n),{n,9}]},CoefficientList[Series[(1-x-x^9)/ den,{x,0,60}],x]] (* _Harvey P. Dale_, May 22 2012 *)

%Y Cf. A026814, A026815.

%Y Cf. For other values of N: A060022 (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), this sequence (N=9), A060029 (N=10).

%K sign,easy

%O 0,5

%A _N. J. A. Sloane_, Mar 17 2001

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Last modified June 12 09:24 EDT 2021. Contains 344946 sequences. (Running on oeis4.)