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Number of partitions of [n] such that for each block the arithmetic mean of the elements is an integer.
1

%I #15 Nov 22 2024 16:18:18

%S 1,1,1,3,6,16,46,145,480,1820,6809,29214,133441,626090,3053048,

%T 16339753,89188931,509642042,3017799873,18798910220,120223747234,

%U 802412450368,5475810949896,39019578827168,285084247621276,2151914766238809,16598498118133839,132851511943710915

%N Number of partitions of [n] such that for each block the arithmetic mean of the elements is an integer.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%e a(0) = 1: the empty partition.

%e a(1) = 1: 1.

%e a(2) = 1: 1|2.

%e a(3) = 3: 123, 13|2, 1|2|3.

%e a(4) = 6: 123|4, 13|24, 13|2|4, 1|234, 1|24|3, 1|2|3|4.

%e 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.

%Y Cf. A000110, A327475, A369074.

%K nonn

%O 0,4

%A _Alois P. Heinz_, Jan 12 2024

%E a(18)-a(27) from _Christian Sievers_, Nov 22 2024