A144881 Lower triangular array called S1hat(3) related to partition number array A144880.

1, 3, 1, 12, 3, 1, 60, 21, 3, 1, 360, 96, 21, 3, 1, 2520, 684, 123, 21, 3, 1, 20160, 4320, 792, 123, 21, 3, 1, 181440, 35640, 5292, 873, 123, 21, 3, 1, 1814400, 293760, 42768, 5616, 873, 123, 21, 3, 1, 19958400, 2881440, 348840, 45684, 5859, 873, 123, 21, 3, 1, 239500800

Offset: 1

Author

Wolfdieter Lang Oct 09 2008

Keywords

• nonn
• easy
• tabl

Comments

If in the partition array M31hat(3):=A144880 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(3). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first columns are A001710(n+1), A144883, A144884,...

Examples

			[1];[3,1];[12,3,1];[60,21,3,1];[360,96,21,3,1];...
		

Links

• W. Lang, First 10 rows of the array and more.
• W. Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.

Crossrefs

A144882 (row sums).

Formula

a(n,m)=sum(product(|S1(3;j,1)|^e(n,m,q,j),j=1..n),q=1..p(n,m)) if n>=m>=1, else 0. Here p(n,m)=A008284(n,m), the number of m parts partitions of n and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. |S1(3,n,1)|= A046089(n,1) = A001710(n+1) = (n+1)!/2.