A067050 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

Offset

0,4

Comments

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

References

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.

Links

Table of n, a(n) for n=0..30.

Example

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

Crossrefs

Row sums give A061296.

Sequence in context: A300003 A259879 A016556 * A001355 A364855 A105531

Adjacent sequences: A067047 A067048 A067049 * A067051 A067052 A067053

Keyword

nonn,tabl

Author

Amarnath Murthy, Dec 30 2001

Extensions

Corrected and extended by Vladeta Jovovic, Dec 31 2001

Status

approved