A144342 Lower triangular array called S2hat(-5) related to partition number array A144341.

1, 5, 1, 55, 5, 1, 935, 80, 5, 1, 21505, 1210, 80, 5, 1, 623645, 29205, 1335, 80, 5, 1, 21827575, 782595, 30580, 1335, 80, 5, 1, 894930575, 27002800, 821095, 31205, 1335, 80, 5, 1, 42061737025, 1058476100, 27963925, 827970, 31205, 1335, 80, 5, 1, 2229272062325, 48782479625

Offset

1,2

Comments

If in the partition array M32khat(-5)= A144341 entries with the same parts number m are summed one obtains this triangle of numbers S2hat(-5). In the same way the Stirling2 triangle A008277 is obtained from the partition array M_3 = A036040.

The first three columns are A008543, A144344, A144345.

Links

Table of n, a(n) for n=1..47.

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(|S2(-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. |S2(-5,n,1)|= A013988(n,1) = A008543(n-1) = (6*n-7)(!^6) (6-factorials) for n>=2 and 1 if n=1.

Example

[1];[5,1];[55,5,1];[935,80,5,1];[21505,1210,80,5,1];...

Crossrefs

Row sums A144343.

A144285 (S2hat(-4)).

Sequence in context: A358112 A051150 A144341 * A144268 A013988 A340472

Adjacent sequences: A144339 A144340 A144341 * A144343 A144344 A144345

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang Oct 09 2008

Status

approved