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A369073
Number of partitions of [n] such that for each block the arithmetic mean of the elements is an integer.
1
1, 1, 1, 3, 6, 16, 46, 145, 480, 1820, 6809, 29214, 133441, 626090, 3053048, 16339753, 89188931, 509642042
OFFSET
0,4
EXAMPLE
a(0) = 1: the empty partition.
a(1) = 1: 1.
a(2) = 1: 1|2.
a(3) = 3: 123, 13|2, 1|2|3.
a(4) = 6: 123|4, 13|24, 13|2|4, 1|234, 1|24|3, 1|2|3|4.
a(5) = 16: 12345, 123|4|5, 1245|3, 135|24, 13|24|5, 135|2|4, 13|2|4|5, 15|234, 1|234|5, 15|24|3, 1|24|35, 1|24|3|5, 1|2|345, 15|2|3|4, 1|2|35|4, 1|2|3|4|5.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Alois P. Heinz, Jan 12 2024
STATUS
approved