A145370 Lower triangular array, called S1hat(-4), related to partition number array A145369.

1, 4, 1, 12, 4, 1, 24, 28, 4, 1, 24, 72, 28, 4, 1, 0, 264, 136, 28, 4, 1, 0, 384, 456, 136, 28, 4, 1, 0, 864, 1344, 712, 136, 28, 4, 1, 0, 576, 4128, 2112, 712, 136, 28, 4, 1, 0, 576, 7488, 7968, 3136, 712, 136, 28, 4, 1, 0, 0, 13248, 20544, 11040, 3136, 712, 136, 28, 4, 1, 0, 0

Offset

1,2

Comments

If in the partition array M31hat(-4):=A145369 entries belonging to partitions 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 column is [1,4,12,24,24,0,0,0,...]= A008279(4,n-1), n>=1.

Links

Table of n, a(n) for n=1..68.

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, Y and e(n,m,q,j) is the exponent of j in the q-th m part partition of n. S1(-4,n,1)= A008279(4,n-1) = [1,4,12,24,24,0,0,0,...], n>=1.

Example

[1];[4,1];[12,4,1];[24,28,4,1];[24,72,28,4,1];...

Crossrefs

A145371 (row sums).

Sequence in context: A175763 A080303 A145369 * A130322 A316232 A372354

Adjacent sequences: A145367 A145368 A145369 * A145371 A145372 A145373

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 17 2008

Status

approved