

A324572


Number of integer partitions of n whose multiplicities (where if x < y the multiplicity of x is counted prior to the multiplicity of y) are equal to the distinct parts in decreasing order.


21



1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 3, 0, 2, 0, 4, 1, 2, 1, 4, 1, 3, 1, 5, 3, 5, 1, 6, 2, 6, 1, 7, 2, 7, 2, 11, 4, 8, 3, 11, 5, 10, 4, 13, 5, 11, 5, 16, 8, 14, 5, 19, 8, 18, 6, 22, 8, 22, 7, 26, 10, 25, 8, 33, 12, 29, 11, 36, 13, 34, 12, 40, 16, 41, 14, 47, 17, 45, 16, 55
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OFFSET

0,5


COMMENTS

These are a kind of selfdescribing partitions (cf. A001462, A304679).
The Heinz numbers of these partitions are given by A324571.
The case where the distinct parts are taken in increasing order is counted by A033461, with Heinz numbers given by A109298.


LINKS



EXAMPLE

The first 19 terms count the following integer partitions:
1: (1)
4: (22)
4: (211)
6: (3111)
8: (41111)
9: (333)
10: (511111)
10: (322111)
12: (6111111)
12: (4221111)
12: (33222)
14: (71111111)
14: (52211111)
16: (811111111)
16: (622111111)
16: (4444)
16: (442222)
17: (43331111)
18: (9111111111)
18: (7221111111)
19: (533311111)


MATHEMATICA

Table[Length[Select[IntegerPartitions[n], Union[#]==Length/@Split[#]&]], {n, 0, 30}]


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



