%I #6 Nov 10 2022 14:55:44
%S 1,2,3,6,10,15,24,35,50,71,98,131,178,234,304,393,503,633,798,992,
%T 1225,1506,1839,2226,2692,3229,3856,4587,5434,6400,7526,8804,10266,
%U 11934,13830,15964,18397,21123,24192,27640,31505,35805,40629,45978,51928,58531,65849
%N Number of partitions of n with nine parts in which no part occurs more than twice.
%H Alois P. Heinz, <a href="/A320597/b320597.txt">Table of n, a(n) for n = 25..10000</a>
%F G.f.: (x^20-x^19-x^18-x^16+x^14+2*x^11+x^10+x^9+x^8-x^6-x^4-x^3-x-1)*x^25 / ((x^2-x+1) *(x^4+x^3+x^2+x+1) *(x^6+x^3+1) *(x^4+1) *(x^6+x^5+x^4+x^3+x^2+x+1) *(x^2+1)^2 *(x^2+x+1)^3 *(x+1)^4 *(x-1)^9).
%t Table[Count[IntegerPartitions[n,{9}],_?(Max[Length/@Split[#]]<3&)],{n,25,75}] (* _Harvey P. Dale_, Nov 10 2022 *)
%Y Column k=9 of A209318.
%K nonn,easy
%O 25,2
%A _Alois P. Heinz_, Oct 16 2018