A275071 Number of set partitions of [n] such that i-j is a multiple of four for all i,j belonging to the same block.

1, 1, 1, 1, 1, 2, 4, 8, 16, 40, 100, 250, 625, 1875, 5625, 16875, 50625, 175500, 608400, 2109120, 7311616, 28543424, 111429136, 435002204, 1698181681, 7336479479, 31695036961, 136928804999, 591559418641, 2792538190620, 13182563408400, 62230116888000

Offset: 0

Author

Alois P. Heinz, Jul 15 2016

Keywords

• nonn

Examples

			a(9) = 40: 159|26|37|48, 15|26|37|48|9, 159|26|37|4|8, 15|26|37|4|8|9, 159|26|3|48|7, 15|26|3|48|7|9, 159|26|3|4|7|8, 15|26|3|4|7|8|9, 159|2|37|48|6, 15|2|37|48|6|9, 159|2|37|4|6|8, 15|2|37|4|6|8|9, 159|2|3|48|6|7, 15|2|3|48|6|7|9, 159|2|3|4|6|7|8, 15|2|3|4|6|7|8|9, 19|26|37|48|5, 1|26|37|48|59, 1|26|37|48|5|9, 19|26|37|4|5|8, 1|26|37|4|59|8, 1|26|37|4|5|8|9, 19|26|3|48|5|7, 1|26|3|48|59|7, 1|26|3|48|5|7|9, 19|26|3|4|5|7|8, 1|26|3|4|59|7|8, 1|26|3|4|5|7|8|9, 19|2|37|48|5|6, 1|2|37|48|59|6, 1|2|37|48|5|6|9, 19|2|37|4|5|6|8, 1|2|37|4|59|6|8, 1|2|37|4|5|6|8|9, 19|2|3|48|5|6|7, 1|2|3|48|59|6|7, 1|2|3|48|5|6|7|9, 19|2|3|4|5|6|7|8, 1|2|3|4|59|6|7|8, 1|2|3|4|5|6|7|8|9.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..739
• Wikipedia, Partition of a set

Crossrefs

Column k=4 of A275069.

Cf. A000110.

Formula

a(n) = Product_{i=0..3} A000110(floor((n+i)/4)).