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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.

%I A274871 #5 Jul 10 2016 14:36:24
%S A274871 1,3,34,102,719,2157,12260,36780,185457,556371,2607078,7821234,
%T A274871 34949443,104848329,453798280,1361394840,5763944693,17291834079,
%U A274871 72085646282,216256938846,891613471047,2674840413141,10940569830060,32821709490180,133469376708409
%N 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.
%H A274871 Alois P. Heinz, <a href="/A274871/b274871.txt">Table of n, a(n) for n = 7..1000</a>
%F A274871 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)).
%e A274871 a(8) = 3: 1|28|3|4|5|6|7, 1|2|3|48|5|6|7, 1|2|3|4|5|68|7.
%e A274871 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.
%Y A274871 Column k=7 of A274537.
%K A274871 nonn,easy
%O A274871 7,2
%A A274871 _Alois P. Heinz_, Jul 09 2016