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Number of partitions of n into 3 distinct parts from [ 1,39 ].
1

%I #16 Aug 06 2024 21:33:09

%S 0,0,0,0,0,0,1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,27,30,33,37,40,44,

%T 48,52,56,61,65,70,75,80,85,91,96,102,108,114,120,127,132,138,143,148,

%U 152,157,160,164,167,170,172,175,176,178,179,180,180,181,180,180,179,178

%N Number of partitions of n into 3 distinct parts from [ 1,39 ].

%C Useful for lottery players playing TAKE 5 in NY (1...39).

%H Sean A. Irvine, <a href="/A034092/b034092.txt">Table of n, a(n) for n = 0..114</a>

%F Coefficient of t^3 in (1+tx)(1+tx^2)(1+tx^3)...(1+tx^39).

%F a(n) = 0 for all n > 114. - _Sean A. Irvine_, Aug 02 2020

%e a(6)=1, since 6 = 1+2+3.

%t CoefficientList[Coefficient[Product[1+t*x^i,{i,39}],t^3],x] (* _Ray Chandler_, Dec 16 2008 *)

%K nonn,easy,fini,full

%O 0,9

%A Edwin Carrasquillo (ecmail(AT)idt.net)

%E Extended by _Ray Chandler_, Dec 16 2008