A274870 Number of set partitions of [n] into exactly six blocks such that all odd elements are in blocks with an odd index and all even elements are in blocks with an even index.

1, 3, 22, 66, 311, 933, 3632, 10896, 38337, 115011, 381594, 1144782, 3664507, 10993521, 34404964, 103214892, 318365333, 955095999, 2918309966, 8754929898, 26585715663, 79757146989, 241208177496, 723624532488, 2182538747689, 6547616243067, 19713018571138

Offset

6,2

Links

Alois P. Heinz, Table of n, a(n) for n = 6..1000

Formula

G.f.: -x^6/((x-1)*(3*x-1)*(2*x+1)*(2*x-1)*(x+1)*(6*x^2-1)*(2*x^2-1)).

Example

a(7) = 3: 17|2|3|4|5|6, 1|2|37|4|5|6, 1|2|3|4|57|6.
a(8) = 22: 13|24|5|6|7|8, 15|24|3|6|7|8, 1|24|35|6|7|8, 15|26|3|4|7|8, 15|2|3|46|7|8, 1|26|35|4|7|8, 1|2|35|46|7|8, 17|26|3|4|5|8, 1|26|37|4|5|8, 1|26|3|4|57|8, 17|2|3|46|5|8, 1|2|37|46|5|8, 1|2|3|46|57|8, 17|28|3|4|5|6, 17|2|3|48|5|6, 17|2|3|4|5|68, 1|28|37|4|5|6, 1|2|37|48|5|6, 1|2|37|4|5|68, 1|28|3|4|57|6, 1|2|3|48|57|6, 1|2|3|4|57|68.

Crossrefs

Column k=6 of A274537.

Sequence in context: A139272 A159345 A006532 * A178492 A005288 A143166

Adjacent sequences: A274867 A274868 A274869 * A274871 A274872 A274873

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 09 2016

Status

approved