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Triangle T(n,r), n>=0, r=n, n-1, ..., 1, 0; where T(n,r) = product of all possible sums of r numbers chosen from [1..n].
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%I #7 Dec 05 2013 19:55:07

%S 1,1,1,3,2,1,6,60,6,1,10,3024,12600,24,1,15,240240,2874009600,

%T 38102400,120,1,21,27907200,129470223826944000,159950125679984640000,

%U 2112397056000,720,1,28,4475671200,1754345199379977566208000000

%N Triangle T(n,r), n>=0, r=n, n-1, ..., 1, 0; where T(n,r) = product of all possible sums of r numbers chosen from [1..n].

%C A dual to the triangle of the absolute values of Stirling numbers (sum of products) of the first kind.

%D Amarnath Murthy, Smarandache Dual Symmetric Functions and Corresponding numbers of the type of Stirling numbers of the first kind, Smarandache Notions Journal, Vol. 12 No. 1-2-3, Spring 2001.

%e E.g. T(4,3) = (1+2+3)*(1+2+4)*(1+3+4)*(2+3+4)=3024.

%Y Row sums give A061296.

%K nonn,tabl

%O 0,4

%A _Amarnath Murthy_, Dec 30 2001

%E Corrected and extended by _Vladeta Jovovic_, Dec 31 2001