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%I #7 Jul 31 2022 18:49:24
%S 0,0,0,0,0,0,1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30,33,36,38,40,
%T 42,43,44,45,45,45,45,44,43,42,40,38,36,33,30,27,24,21,19,16,14,12,10,
%U 8,7,5,4,3,2,1,1,0,0,0,0,0,0
%N Number of partitions of n into 3 distinct parts from [ 1,20 ].
%F Coefficient of t^3 in (1+tx)(1+tx^2)(1+tx^3)...(1+tx^20).
%t Table[Count[IntegerPartitions[n,{3}],_?(Length[Union[#]]==3&&Max[#]<21&)],{n,0,70}] (* _Harvey P. Dale_, Jul 31 2022 *)
%K nonn
%O 0,9
%A _N. J. A. Sloane_.