%I #7 Jul 10 2016 16:10:48
%S 1,0,1,3,35,226,3632,36780,770481,10677444,277114769,4882093495,
%T 151410615066,3238949008872,116936529884088,2943848265346408,
%U 121318690777898613,3513774792447267240,162794429514873454259,5332375501915984656921,274393112247007415104839
%N Number of set partitions of [2n] into exactly n 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="/A274875/b274875.txt">Table of n, a(n) for n = 0..300</a>
%F a(n) = A274537(2n,n).
%e a(2) = 1: 13|24.
%e a(3) = 3: 13|246|5, 15|246|3, 1|246|35.
%e a(4) = 35: 135|246|7|8, 137|246|5|8, 13|246|57|8, 137|248|5|6, 137|24|5|68, 13|248|57|6, 13|24|57|68, 157|246|3|8, 15|246|37|8, 157|248|3|6, 157|24|3|68, 15|248|37|6, 15|24|37|68, 17|246|35|8, 1|246|357|8, 17|248|35|6, 17|24|35|68, 1|248|357|6, 1|24|357|68, 157|268|3|4, 157|26|3|48, 15|268|37|4, 15|26|37|48, 157|28|3|46, 157|2|3|468, 15|28|37|46, 15|2|37|468, 17|268|35|4, 17|26|35|48, 1|268|357|4, 1|26|357|48, 17|28|35|46, 17|2|35|468, 1|28|357|46, 1|2|357|468.
%Y Cf. A274537.
%K nonn
%O 0,4
%A _Alois P. Heinz_, Jul 09 2016