A145367 Lower triangular array, called S1hat(-3), related to partition number array A145366.

1, 3, 1, 6, 3, 1, 6, 15, 3, 1, 0, 24, 15, 3, 1, 0, 54, 51, 15, 3, 1, 0, 36, 108, 51, 15, 3, 1, 0, 36, 198, 189, 51, 15, 3, 1, 0, 0, 360, 360, 189, 51, 15, 3, 1, 0, 0, 324, 846, 603, 189, 51, 15, 3, 1, 0, 0, 216, 1296, 1332, 603, 189, 51, 15, 3, 1, 0, 0, 216, 2484, 2754, 2061, 603, 189

Offset

1,2

Comments

If in the partition array M31hat(-3):=A145366 entries belonging to partitions 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 column is [1,3,6,6,0,0,0,...]= A008279(3,n-1), n>=1.

Links

Table of n, a(n) for n=1..74.

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)= A008279(3,n-1) = [1,3,6,6,0,0,0,...], n>=1.

Example

[1];[3,1];[6,3,1];[6,15,3,1];[0,24,15,3,1];...

Crossrefs

A145368 (row sums).

Sequence in context: A072361 A341219 A145366 * A124928 A249250 A122432

Adjacent sequences: A145364 A145365 A145366 * A145368 A145369 A145370

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 17 2008

Status

approved