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Expansion of 1/((1-x^3)(1-x^4)(1-x^5)(1-x^12)).
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%I #11 Aug 19 2022 13:58:11

%S 1,0,0,1,1,1,1,1,2,2,2,2,4,3,3,5,5,5,6,6,8,8,8,9,12,11,11,14,15,15,17,

%T 17,20,21,21,23,27,26,27,31,33,33,36,37,41,43,43,46,52,51,53,58,61,62,

%U 66,68,73,76,77,81,89,88

%N Expansion of 1/((1-x^3)(1-x^4)(1-x^5)(1-x^12)).

%C Number of partitions of n into parts 3, 4, 5, and 12. - _Vincenzo Librandi_, Jun 03 2014

%H Vincenzo Librandi, <a href="/A029250/b029250.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,1,1,1,0,-1,-1,-1,0,0,2,0,0,-1,-1,-1,0,1,1,1,0,0,-1).

%F G.f.: 1/((1-x^3)*(1-x^4)*(1-x^5)*(1-x^12)).

%F a(n) = a(n-3)+a(n-4)+a(n-5)-a(n-7)-a(n-8)-a(n-9)+2*a(n-12)-a(n-15)-a(n-16)-a(n-17)+a(n-19)+a(n-20)+a(n-21)-a(n-24). - _Wesley Ivan Hurt_, Aug 19 2022

%t CoefficientList[Series[1/((1 - x^3) (1 - x^4) (1 - x^5) (1 - x^12)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jun 03 2014 *)

%o (PARI) Vec(1/((1-x^3)*(1-x^4)*(1-x^5)*(1-x^12)) + O(x^80)) \\ _Jinyuan Wang_, Mar 12 2020

%K nonn,easy

%O 0,9

%A _N. J. A. Sloane_