A145373 Lower triangular array, called S1hat(-5), related to partition number array A145372.

1, 5, 1, 20, 5, 1, 60, 45, 5, 1, 120, 160, 45, 5, 1, 120, 820, 285, 45, 5, 1, 0, 1920, 1320, 285, 45, 5, 1, 0, 6600, 5420, 1945, 285, 45, 5, 1, 0, 9600, 23600, 7920, 1945, 285, 45, 5, 1, 0, 21600, 66600, 41100, 11045, 1945, 285, 45, 5, 1, 0, 14400, 189600, 151600, 53600, 11045

Offset

1,2

Comments

If in the partition array M31hat(-5):=A145372 entries belonging to partitions 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 column is [1,5,20,60,120,120,0,0,0,...]= A008279(5,n-1), n>=1.

Links

Table of n, a(n) for n=1..61.

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)= A008279(5,n-1) = [1,5,20,60,120,120,0,0,0,...], n>=1.

Example

[1];[5,1];[20,5,1];[60,45,5,1];[120,160,45,5,1];...

Crossrefs

A145374 (row sums).

Sequence in context: A066480 A136394 A145372 * A088577 A368380 A127561

Adjacent sequences: A145370 A145371 A145372 * A145374 A145375 A145376

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 17 2008

Status

approved