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%I #5 Jul 10 2016 14:32:54
%S 1,3,22,66,311,933,3632,10896,38337,115011,381594,1144782,3664507,
%T 10993521,34404964,103214892,318365333,955095999,2918309966,
%U 8754929898,26585715663,79757146989,241208177496,723624532488,2182538747689,6547616243067,19713018571138
%N 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.
%H Alois P. Heinz, <a href="/A274870/b274870.txt">Table of n, a(n) for n = 6..1000</a>
%F 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)).
%e a(7) = 3: 17|2|3|4|5|6, 1|2|37|4|5|6, 1|2|3|4|57|6.
%e 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.
%Y Column k=6 of A274537.
%K nonn,easy
%O 6,2
%A _Alois P. Heinz_, Jul 09 2016
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