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Expansion of 1/((1-x^7)*(1-x^8)*(1-x^9)*(1-x^10)).
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%I #20 Jan 20 2025 03:55:56

%S 1,0,0,0,0,0,0,1,1,1,1,0,0,0,1,1,2,2,2,1,1,1,1,2,3,3,3,3,3,2,3,3,4,4,

%T 5,5,5,5,5,5,6,6,7,7,8,8,8,8,9,9,10,10,11,11,12,12,13,13,14,14,15,15,

%U 16,17,18,18,19,19,20,20,22,22,24,24,25,25,26,27

%N Expansion of 1/((1-x^7)*(1-x^8)*(1-x^9)*(1-x^10)).

%C a(n) is the number of partitions of n into parts 7, 8, 9, and 10. - _Joerg Arndt_, Jan 20 2025

%H <a href="/index/Rec#order_34">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,1,1,1,1,0,0,0,0,-1,-1,-2,-1,-1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,-1).

%F There is a lengthy linear recurrence that generates the terms of this sequence, but it requires 34 initial terms to be provided and it requires reference to 14 prior terms to calculate the next term. [_Harvey P. Dale_, Feb 21 2012]

%t CoefficientList[Series[1/((1-x^7)(1-x^8)(1-x^9)(1-x^10)),{x,0,80}],x] (* _Harvey P. Dale_, Feb 21 2012 *)

%K nonn,easy

%O 0,17

%A _N. J. A. Sloane_.