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%I #6 Jun 10 2018 13:32:15
%S 1,1,1,2,3,7,14,33,84,204,627,1558,5692,14402,60752,155828,747046,
%T 1937292,10385051,27176489,161160411,424958631,2760858706,7327447983,
%U 51762453941,138150105263,1054164297384,2827224795106,23174732414244,62420125297576,546984814641114
%N Number of set partitions of [n] with alternating parity of elements and exactly ceiling(n/2) blocks.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F a(n) = A274581(n,ceiling(n/2)).
%e a(5) = 7: 123|4|5, 12|34|5, 12|3|45, 1|234|5, 145|2|3, 1|2|345, 1|23|45.
%Y Cf. A274581.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Jun 10 2018