A275072 Number of set partitions of [n] such that i-j is a multiple of five for all i,j belonging to the same block.

1, 1, 1, 1, 1, 1, 2, 4, 8, 16, 32, 80, 200, 500, 1250, 3125, 9375, 28125, 84375, 253125, 759375, 2632500, 9126000, 31636800, 109674240, 380204032, 1484258048, 5794315072, 22620114608, 88305447412, 344730881243, 1489305334237, 6434092503083, 27796547414797

Offset

0,7

Links

Alois P. Heinz, Table of n, a(n) for n = 0..772

Wikipedia, Partition of a set

Formula

a(n) = Product_{i=0..4} A000110(floor((n+i)/5)).

Example

a(9) = 16: 16|27|38|49|5, 16|27|38|4|5|9, 16|27|3|49|5|8, 16|27|3|4|5|8|9, 16|2|38|49|5|7, 16|2|38|4|5|7|9, 16|2|3|49|5|7|8, 16|2|3|4|5|7|8|9, 1|27|38|49|5|6, 1|27|38|4|5|6|9, 1|27|3|49|5|6|8, 1|27|3|4|5|6|8|9, 1|2|38|49|5|6|7, 1|2|38|4|5|6|7|9, 1|2|3|49|5|6|7|8, 1|2|3|4|5|6|7|8|9.

Crossrefs

Column k=5 of A275069.

Cf. A000110.

Sequence in context: A076766 A344492 A359389 * A290555 A035523 A290301

Adjacent sequences: A275069 A275070 A275071 * A275073 A275074 A275075

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2016

Status

approved