OFFSET
1,2
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(-3;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(-3;n,k) is summed over those k with fixed number of parts m one obtains triangle S2hat(-3):= A144280(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_{j=1..n} |S2(-3,j,1)|^e(n,k,j), with |S2(-3,n,1)|= A008545(n-1) = (4*n-5)(!^4) (4-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) = 9 = |S2(-3,2,1)|^2. The relevant partition of 4 is (2^2).
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Oct 09 2008
STATUS
approved