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

0,6

Links

Alois P. Heinz, Table of n, a(n) for n = 0..739

Wikipedia, Partition of a set

Formula

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

Example

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.

Crossrefs

Column k=4 of A275069.

Cf. A000110.

Sequence in context: A350495 A337581 A259377 * A018575 A013116 A012912

Adjacent sequences: A275068 A275069 A275070 * A275072 A275073 A275074

Keyword

nonn

Author

Alois P. Heinz, Jul 15 2016

Status

approved