A275070 Number of set partitions of [n] such that i-j is a multiple of three for all i,j belonging to the same block.

1, 1, 1, 1, 2, 4, 8, 20, 50, 125, 375, 1125, 3375, 11700, 40560, 140608, 548912, 2142868, 8365427, 36140293, 156133187, 674526133, 3184194060, 15031429200, 70957944000, 362451121200, 1851389821260, 9456845543523, 51863510753775, 284431392616875

Offset: 0

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Examples

			a(7) = 20: 147|25|36, 14|25|36|7, 147|25|3|6, 14|25|3|6|7, 147|2|36|5, 14|2|36|5|7, 147|2|3|5|6, 14|2|3|5|6|7, 17|25|36|4, 1|25|36|47, 1|25|36|4|7, 17|25|3|4|6, 1|25|3|47|6, 1|25|3|4|6|7, 17|2|36|4|5, 1|2|36|47|5, 1|2|36|4|5|7, 17|2|3|4|5|6, 1|2|3|47|5|6, 1|2|3|4|5|6|7.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..699
• Wikipedia, Partition of a set

Crossrefs

Column k=3 of A275069.

Cf. A000110.

Formula

a(n) = Product_{i=0..2} A000110(floor((n+i)/3)).