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

1,2

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,...

Links

Table of n, a(n) for n=1..56.

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.

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.

Example

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

Crossrefs

A144882 (row sums).

Sequence in context: A178619 A124572 A144880 * A121420 A366892 A283085

Adjacent sequences: A144878 A144879 A144880 * A144882 A144883 A144884

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 09 2008

Status

approved