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

Author

Alois P. Heinz, Jul 09 2016

Keywords

• nonn
• easy

Examples

			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.
		

Links

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

Crossrefs

Column k=7 of A274537.

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)).