A145357 Lower triangular array, called S1hat(6), related to partition number array A145356.

1, 6, 1, 42, 6, 1, 336, 78, 6, 1, 3024, 588, 78, 6, 1, 30240, 6804, 804, 78, 6, 1, 332640, 62496, 8316, 804, 78, 6, 1, 3991680, 753984, 85176, 9612, 804, 78, 6, 1, 51891840, 8273664, 1021608, 94248, 9612, 804, 78, 6, 1, 726485760, 109118016, 11394432, 1157688, 102024

Offset: 1

Author

Wolfdieter Lang, Oct 17 2008

Keywords

• nonn
• easy
• tabl

Comments

If in the partition array M31hat(6):=A145356 entries belonging to partitions with the same parts number m are summed one obtains this triangle of numbers S1hat(6). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first columns are A001725(n+4), A145359, A145360,...

Examples

			Triangle begins:
  [1];
  [6,1];
  [42,6,1];
  [336,78,6,1];
  [3024,588,78,6,1];
  ...
		

Links

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

Crossrefs

Cf. A145358 (row sums).

Formula

a(n,m) = sum(product(|S1(6;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(6,n,1)|= A049374(n,1) = A001725(n+4) = (n+4)!/5!.