OFFSET
1,2
COMMENTS
For the A-St order of partitions see the Abramowitz-Stegun reference given in A117506.
Partition number array M_3(6), the k=6 member in the family of a generalization of the multinomial number arrays M_3 = M_3(1) = A036040.
The sequence of row lengths is A000041 (partition numbers) [1, 2, 3, 5, 7, 11, 15, 22, 30, 42, ...].
The S2(6,n,m):=A049385(n,m) numbers (generalized Stirling2 numbers) are obtained by summing in row n all numbers with the same part number m. In the same manner the S2(n,m) (Stirling2) numbers A008277 are obtained from the partition array M_3= A036040.
a(n,k) enumerates unordered forests of increasing 6-ary trees related to the k-th partition of n in the A-St order. The m-forest is composed of m such trees, with m the number of parts of the partition.
LINKS
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Wolfdieter Lang, First 10 rows and more.
FORMULA
EXAMPLE
[1]; [6,1]; [66,18,1]; [1056,264,108,36,1]; [22176,5280,3960,660,540,60,1]; ...
There are a(4,3) = 108 = 3*6^2 unordered 2-forests with 4 vertices, composed of two 6-ary increasing trees, each with two vertices: there are 3 increasing labelings (1,2)(3,4); (1,3)(2,4); (1,4)(2,3) and each tree comes in six versions from the 6-ary structure.
CROSSREFS
KEYWORD
nonn,easy,tabf
AUTHOR
Wolfdieter Lang, Nov 13 2007
STATUS
approved