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Number of set partitions of [2n] having exactly n pairs (m,m+1) such that m+1 is in some block b and m is in block b+1.
1

%I #5 Mar 27 2016 14:31:21

%S 1,0,0,1,10,127,1650,23258,361154,6131236,113042841,2248848796,

%T 47985568177,1092290052791,26397613960112,674479517926073,

%U 18153075875657428,512977569857121559,15176209471995304906,468847646698743759887,15090613008931715532300

%N Number of set partitions of [2n] having exactly n pairs (m,m+1) such that m+1 is in some block b and m is in block b+1.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A270953(2n,n).

%e a(3) = 1: 136|25|4.

%e a(4) = 10: 1358|247|6, 1368|257|4, 136|258|47, 136|25|48|7, 138|257|46, 13|258|47|6, 138|27|46|5, 158|247|36, 15|248|37|6, 18|247|36|5.

%e a(5) = 127: 1247(10)|369|58, 1247|36(10)|59|8, 124(10)|369|58|7, ..., 1(10)|269|358|47, 1|26(10)|359|48|7, 1(10)|29|358|47|6.

%Y Cf. A270953.

%K nonn

%O 0,5

%A _Alois P. Heinz_, Mar 26 2016