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Expansion of 1/((1-x^2)(1-x^3)(1-x^5)(1-x^9)).
1

%I #15 Mar 18 2020 08:10:04

%S 1,0,1,1,1,2,2,2,3,4,4,5,6,6,8,9,9,11,13,13,16,17,18,21,23,24,27,30,

%T 31,35,38,39,44,47,49,54,58,60,66,70,73,79,84,87,94,100,103,111,117,

%U 121,130,136,141,150,158,163,173,181,187,198,207,213,225,235,242,255,265,273,287,298,307,321,334

%N Expansion of 1/((1-x^2)(1-x^3)(1-x^5)(1-x^9)).

%C Number of partitions of n into parts 2, 3, 5, and 9. - _Joerg Arndt_, Aug 16 2013

%H Vincenzo Librandi, <a href="/A029146/b029146.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,-1,-1,1,1,-1,-1,0,0,0,1,1,0,-1).

%t CoefficientList[Series[1 / ((1 - x^2) (1 - x^3) (1 - x^5) (1 - x^9)), {x, 0, 80}], x] (* _Vincenzo Librandi_, Aug 17 2013 *)

%o (PARI) a(n)=round((n\3+1)*(-2)^(n%3%2)/27+(n%5<2)*(-1)^(n%5)/5+(2*n+19)*(2*n^2+38*n+121)/6480) \\ _Tani Akinari_, Aug 15 2013

%o (PARI) Vec( 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^9)) + O(x^66) ) \\ _Joerg Arndt_, Aug 16 2013

%K nonn,easy

%O 0,6

%A _N. J. A. Sloane_