OFFSET
0,8
COMMENTS
The sequence of row lengths of this array is A187446(n)+1.
The considered multiset representatives are defined by certain partitions, taken in Abramowitz-Stegun (A-St)order. For this order see A036036, and for these partitions see A176723, as well as A176725 with a link.
This investigation was inspired by M. Griffiths and I. Mezo (see reference in A176725).
FORMULA
a(n,l), l=0,..,A187446(n), is the number "multiset choose l" for the multiset defined by the n-th multiset repetition class defining partition in A-St order.
a(n,0)=1, n>=0, by definition.
EXAMPLE
[1],
[1, 1],
[1, 1, 1],
[1, 2, 1],
[1, 1, 1, 1],
[1, 2, 2, 1],
[1, 1, 1, 1, 1],
...
a(5,2)=2 because the 5th multiset repetition class defining partition in A-St order is 1^2,2 (a partition of N=4) which defines the 3-multiset {1,1,2}, and there are 2 possibilities to pick 2 elements from the multiset, namely 1,1 and 1,2.
a(6,4)=1 from picking all 4 elements from the 6th multiset representative in A-St order: {1,1,1,1}.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Wolfdieter Lang, Mar 14 2011
EXTENSIONS
Changed in response to a comment by Franklin T. Adams-Watters. - Wolfdieter Lang, Apr 02 2011
STATUS
approved