OFFSET
1,8
COMMENTS
The relevant partitions of n have exactly k parts.
The number of multiplicity multisets of size k met by a positive even number of partitions of n is A337584(n, k) - T(n, k).
LINKS
Álvar Ibeas, First 72 rows, flattened
Álvar Ibeas, First 30 rows
EXAMPLE
The 3 = A008284(6, 2) partitions of 6 into 2 parts show 2 = A337584(6, 2) different multiplicity multisets: (1, 1) is attained by two of those partitions ((5, 1) and (4, 2)) and the other (2) just by one, (3, 3). Then, T(6, 2) = 1.
Triangle begins:
k: 1 2 3 4 5 6 7 8 9 10
--------------------
n=1: 1
n=2: 1 1
n=3: 1 1 1
n=4: 1 2 1 1
n=5: 1 0 0 1 1
n=6: 1 1 3 2 1 1
n=7: 1 1 2 1 2 1 1
n=8: 1 2 1 3 3 2 1 1
n=9: 1 0 3 0 3 3 2 1 1
n=10: 1 1 0 3 3 3 3 2 1 1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Álvar Ibeas, Sep 02 2020
STATUS
approved