OFFSET
1,4
COMMENTS
Each partition of n, ordered as in Abramowitz-Stegun (A-St order; for the reference see A134278), is mapped to a nonnegative integer a(n,k) =: M32hat(-1;n,k) with the k-th partition of n in A-St order.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42,...].
If M32hat(-1;n,k) is summed over those k with fixed number of parts m one obtains triangle S2hat(-1):= A144270(n,m).
LINKS
Wolfdieter Lang, First 10 rows of the array and more.
Wolfdieter Lang, Combinatorial Interpretation of Generalized Stirling Numbers, J. Int. Seqs. Vol. 12 (2009) 09.3.3.
FORMULA
a(n,k)= product(|S2(-1,j,1)|^e(n,k,j),j=1..n) with |S2(-1,n,1)|= A001147(n-1) = (2*n-3)(!^2) (2-factorials) for n>=2 and 1 if n=1 and the exponent e(n,k,j) of j in the k-th partition of n in the A-St ordering of the partitions of n.
EXAMPLE
a(4,3)= 1 = |S2(-1,2,1)|^2. The relevant partition of 4 is (2^2).
[1]; [1,1]; [3,1,1]; [15,3,1,1,1]; [105,15,3,3,1,1,1]; ... [From Wolfdieter Lang, Oct 23 2008]
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Oct 09 2008
EXTENSIONS
Corrected all entries. Wolfdieter Lang, Oct 23 2008
STATUS
approved