|
| |
|
|
A144880
|
|
Partition number array, called M31hat(3).
|
|
4
| |
|
|
1, 3, 1, 12, 3, 1, 60, 12, 9, 3, 1, 360, 60, 36, 12, 9, 3, 1, 2520, 360, 180, 144, 60, 36, 27, 12, 9, 3, 1, 20160, 2520, 1080, 720, 360, 180, 144, 108, 60, 36, 27, 12, 9, 3, 1, 181440, 20160, 7560, 4320, 3600, 2520, 1080, 720, 540, 432, 360, 180, 144, 108, 81, 60, 36, 27
(list; graph; refs; listen; history; internal format)
|
|
|
|
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) =: M31hat(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,...].
This is the third (K=3) member of a family of partition number arrays: A107106, A134133,...
|
|
|
LINKS
| 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,k)= product(|S1(3;j,1)|^e(n,k,j),j=1..n) with |S1(3;n,1)|= A046089(1,n) = [1,3,12,60,...], 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
| [1];[3,1];[12,3,1];[60,12,9,3,1];[360,60,36,12,9,3,1];...
a(4,3)= 9 = |S1(3;2,1)|^2. The relevant partition of 4 is (2^2).
|
|
|
CROSSREFS
| A144882 (row sums).
A134133 (M31hat(2) array). A144885 (M31hat(4) array).
Sequence in context: A118020 A178619 A124572 * A144881 A121420 A117375
Adjacent sequences: A144877 A144878 A144879 * A144881 A144882 A144883
|
|
|
KEYWORD
| nonn,easy,tabf
|
|
|
AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Oct 09 2008
|
| |
|
|
