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

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..772
• Wikipedia, Partition of a set

Crossrefs

Column k=5 of A275069.

Cf. A000110.

Formula

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