

A176725


Number of ways to choose one element from the multiset corresponding to the kth multiset repetition class defining partition of n in canonical AbramowitzStegun order.


8



0, 1, 1, 2, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 2, 2, 1, 3, 3, 2, 2, 2, 1, 4, 3, 3, 2, 2, 2, 1, 4, 3, 3, 2, 2, 2, 1, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1, 4, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1, 4, 4, 3, 3, 3, 2, 3, 2, 2, 2, 1, 5, 4, 3, 4, 3, 3, 3, 2, 3, 2, 3, 2, 2, 2, 1, 5, 4, 4, 4, 3, 4, 3, 3, 3, 2, 3, 2, 3, 2, 2, 2, 1
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OFFSET

0,4


COMMENTS

This array a(n,k), called (Multiset choose 1), is also denoted by MS(1;n,k).
MS(1;n,k) gives the number of ways to choose one element from the multiset encoded by the kth multiset repetition class defining partition of n. a(n,k)=MS(1;n,k) is the largest part in the kth multiset defining partition of n, i.e., the largest element in the multiset. The ASt order for partitions is used. For n=0 the empty multiset appears.
The row lengths of this array are A007294(n).
Multisets are sets in which the elements are allowed to appear more than once. Representatives of repetition classes can be characterized as certain partitions of the nonnegative integers n. For the characteristic array of these partitions of n in ASt order see A176723.
This is the first member of an lfamily of arrays for multiset choose l, called MS(l;n,k). This investigation was stimulated by the quoted Griffiths and Mező paper.


LINKS

Table of n, a(n) for n=0..104.
M. Griffiths and I. Mező, A Generalization of Stirling Numbers of the Second Kind via a Special Multiset, Journal of Integer Sequences 13 (2010) 10.2.5.
W. Lang, First 15 rows and corresponding multisets.


FORMULA

a(n,k)= largest part in the kth multiset repetition class defining partition of n>=1. a(0,1):=0. See the characteristic array A176723 in order to find this partition.
a(n,k) = largest element of the kth multiset repetition class representative in row n>=1, a(0,1):=0.


EXAMPLE

[0],
[1],
[1],
[2,1],
[2,1],
[2,1],
[3,2,2,1],
[3,2,2,1],
[3,2,2,1],
[3,3,2,2,2,1],
...
a(6,2)=MS(1;6,2)=2 because the second multiset repetition class defining partition of n=6 is [1^2,2^2] (from the characteristic array A176723) encoding the 4multiset representative {1,1,2,2}, and there are 2 ways to choose 1 element from this set.


CROSSREFS

Sequence in context: A167970 A126433 A237271 * A085029 A185318 A008622
Adjacent sequences: A176722 A176723 A176724 * A176726 A176727 A176728


KEYWORD

nonn,tabf,easy


AUTHOR

Wolfdieter Lang, Jul 14 2010


EXTENSIONS

Changed in response to comments by Franklin T. AdamsWatters  Wolfdieter Lang, Apr 02 2011


STATUS

approved



