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Number of set partitions of [2n+1] such that n+1 is the largest element of the last block.
2

%I #5 Apr 11 2016 09:05:14

%S 1,1,6,63,1039,24190,745107,29058813,1389893708,79588371929,

%T 5353760622719,416660175523064,37047640989016445,3724084616168887373,

%U 419437505978046355690,52523298180976612585435,7263669823685446959438851,1102849583101324096499809166

%N Number of set partitions of [2n+1] such that n+1 is the largest element of the last block.

%C Each set partition is written as a sequence of blocks, ordered by the smallest elements in the blocks.

%H Alois P. Heinz, <a href="/A271607/b271607.txt">Table of n, a(n) for n = 0..200</a>

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

%F a(n) = A271466(2n+1,n+1).

%e a(0) = 1: 1.

%e a(1) = 1: 13|2.

%e a(2) = 6: 1245|3, 145|23, 145|2|3, 14|25|3, 15|24|3, 1|245|3.

%e a(3) = 63: 123567|4, 12567|34, 12567|3|4, 1256|37|4, ..., 1|26|357|4, 17|2|356|4, 1|27|356|4, 1|2|3567|4.

%Y Cf. A271466.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Apr 10 2016