A144891 Lower triangular array called S1hat(5) related to partition number array A144890.

1, 5, 1, 30, 5, 1, 210, 55, 5, 1, 1680, 360, 55, 5, 1, 15120, 3630, 485, 55, 5, 1, 151200, 29820, 4380, 485, 55, 5, 1, 1663200, 321300, 39570, 5005, 485, 55, 5, 1, 19958400, 3225600, 421800, 43320, 5005, 485, 55, 5, 1, 259459200, 38808000, 4265100, 470550, 46445, 5005

Offset

1,2

Comments

If in the partition array M31hat(5):=A144890 entries with the same parts number m are summed one obtains this triangle of numbers S1hat(5). In the same way the signless Stirling1 triangle |A008275| is obtained from the partition array M_2 = A036039.

The first columns are A001720(n+3)=(n+3)!/4!, A144893, A144894,...

Links

Table of n, a(n) for n=1..51.

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(5;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(5,n,1)|= A049353(n,1) = A001720(n+3) = (n+3)!/4!.

Example

[1];[5,1];[30,5,1];[210,55,5,1];[1680,360,55,5,1];...

Crossrefs

A144892 (row sums).

Sequence in context: A232015 A214882 A144890 * A135892 A049460 A145926

Adjacent sequences: A144888 A144889 A144890 * A144892 A144893 A144894

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 09 2008

Status

approved