_Amarnath Murthy (amarnath_murthy(AT)yahoo.com), _, Dec 30 2001

Corrected and extended by _Vladeta Jovovic (vladeta(AT)eunet.rs), _, Dec 31 2001

editing

approved

M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/">Smarandache Notions Journal</a>

approved

editing

nonn,tabl,new

Corrected and extended by Vladeta Jovovic (vladeta(AT)Euneteunet.yurs), Dec 31 2001

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.

nonn,tabl,new

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].

1, 1, 1, 3, 2, 1, 6, 60, 6, 1, 10, 3024, 12600, 24, 1, 15, 240240, 2874009600, 38102400, 120, 1, 21, 27907200, 129470223826944000, 159950125679984640000, 2112397056000, 720, 1, 28, 4475671200, 1754345199379977566208000000

0,4

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

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.

M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/">Smarandache Notions Journal</a>

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

Row sums give A061296.

nonn,tabl

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 30 2001

Corrected and extended by Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 31 2001

approved