A369073 Number of partitions of [n] such that for each block the arithmetic mean of the elements is an integer.

1, 1, 1, 3, 6, 16, 46, 145, 480, 1820, 6809, 29214, 133441, 626090, 3053048, 16339753, 89188931, 509642042, 3017799873, 18798910220, 120223747234, 802412450368, 5475810949896, 39019578827168, 285084247621276, 2151914766238809, 16598498118133839, 132851511943710915

Offset

0,4

Links

Table of n, a(n) for n=0..27.

Wikipedia, Partition of a set

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

Cf. A000110, A327475, A369074.

Sequence in context: A220184 A007002 A305136 * A300355 A360865 A378801

Adjacent sequences: A369070 A369071 A369072 * A369074 A369075 A369076

Keyword

nonn

Author

Alois P. Heinz, Jan 12 2024

Extensions

a(18)-a(27) from Christian Sievers, Nov 22 2024

Status

approved