A274871 Number of set partitions of [n] into exactly seven 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, 34, 102, 719, 2157, 12260, 36780, 185457, 556371, 2607078, 7821234, 34949443, 104848329, 453798280, 1361394840, 5763944693, 17291834079, 72085646282, 216256938846, 891613471047, 2674840413141, 10940569830060, 32821709490180, 133469376708409

Offset

7,2

Links

Alois P. Heinz, Table of n, a(n) for n = 7..1000

Formula

G.f.: x^7/((x-1)*(3*x-1)*(2*x+1)*(2*x-1)*(x+1)*(12*x^2-1) *(6*x^2-1)* (2*x^2-1)).

Example

a(8) = 3: 1|28|3|4|5|6|7, 1|2|3|48|5|6|7, 1|2|3|4|5|68|7.
a(9) = 34: 13|24|5|6|7|8|9, 15|24|3|6|7|8|9, 1|24|35|6|7|8|9, 15|26|3|4|7|8|9, 15|2|3|46|7|8|9, 1|26|35|4|7|8|9, 1|2|35|46|7|8|9, 17|26|3|4|5|8|9, 1|26|37|4|5|8|9, 1|26|3|4|57|8|9, 17|2|3|46|5|8|9, 1|2|37|46|5|8|9, 1|2|3|46|57|8|9, 17|28|3|4|5|6|9, 17|2|3|48|5|6|9, 17|2|3|4|5|68|9, 1|28|37|4|5|6|9, 1|2|37|48|5|6|9, 1|2|37|4|5|68|9, 1|28|3|4|57|6|9, 1|2|3|48|57|6|9, 1|2|3|4|57|68|9, 19|28|3|4|5|6|7, 1|28|39|4|5|6|7, 1|28|3|4|59|6|7, 1|28|3|4|5|6|79, 19|2|3|48|5|6|7, 1|2|39|48|5|6|7, 1|2|3|48|59|6|7, 1|2|3|48|5|6|79, 19|2|3|4|5|68|7, 1|2|39|4|5|68|7, 1|2|3|4|59|68|7, 1|2|3|4|5|68|79.

Crossrefs

Column k=7 of A274537.

Sequence in context: A086488 A195021 A344429 * A042041 A180775 A243011

Adjacent sequences: A274868 A274869 A274870 * A274872 A274873 A274874

Keyword

nonn,easy

Author

Alois P. Heinz, Jul 09 2016

Status

approved