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%I #5 Jul 10 2016 14:30:34
%S 1,2,13,26,113,226,833,1666,5649,11298,36561,73122,230161,460322,
%T 1424401,2848802,8720657,17441314,53021969,106043938,320925969,
%U 641851938,1936736529,3873473058,11665150225,23330300450,70169841937,140339683874,421734846737
%N Number of set partitions of [n] into exactly five 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="/A274869/b274869.txt">Table of n, a(n) for n = 5..1000</a>
%F G.f.: x^5/((x-1)*(2*x-1)*(x+1)*(6*x^2-1)*(2*x^2-1)).
%e a(6) = 2: 1|26|3|4|5, 1|2|3|46|5.
%e a(7) = 13: 13|24|5|6|7, 15|24|3|6|7, 1|24|35|6|7, 15|26|3|4|7, 15|2|3|46|7, 1|26|35|4|7, 1|2|35|46|7, 17|26|3|4|5, 1|26|37|4|5, 1|26|3|4|57, 17|2|3|46|5, 1|2|37|46|5, 1|2|3|46|57.
%Y Column k=5 of A274537.
%K nonn,easy
%O 5,2
%A _Alois P. Heinz_, Jul 09 2016
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