A144886 Lower triangular array called S1hat(4) related to partition number array A144885.

1, 4, 1, 20, 4, 1, 120, 36, 4, 1, 840, 200, 36, 4, 1, 6720, 1720, 264, 36, 4, 1, 60480, 12480, 2040, 264, 36, 4, 1, 604800, 118560, 16000, 2296, 264, 36, 4, 1, 6652800, 1081920, 149600, 17280, 2296, 264, 36, 4, 1, 79833600, 11793600, 1362240, 163680, 18304, 2296, 264

Offset

1,2

Comments

If in the partition array M31hat(4):=A144885 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(4). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first columns are A001715(n+2), A144888, A144889,...

Links

Table of n, a(n) for n=1..52.

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(4;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(4,n,1)|= A049352(n,1) = A001715(n+2) = (n+2)!/3!.

Example

[1];[4,1];[20,4,1];[120,36,4,1];[840,200,36,4,1];...

Crossrefs

A144887 (row sums).

Sequence in context: A333273 A128041 A144885 * A117380 A185420 A167432

Adjacent sequences: A144883 A144884 A144885 * A144887 A144888 A144889

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 09 2008

Status

approved