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A297924 Number of set partitions of [2n] in which the size of the last block is n.

%I A297924 #13 May 20 2018 11:36:39
%S A297924 1,1,4,20,125,952,8494,86025,969862,12020580,162203607,2363458396,
%T A297924 36930606254,615302885459,10878670826170,203268056115256,
%U A297924 3999642836434361,82617423216826640,1786559190116778030,40344863179696283037,949348461372003462390
%N A297924 Number of set partitions of [2n] in which the size of the last block is n.
%C A297924 The blocks are ordered with increasing least elements.
%C A297924 a(0) = 1 by convention.
%H A297924 Alois P. Heinz, <a href="/A297924/b297924.txt">Table of n, a(n) for n = 0..466</a>
%H A297924 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A297924 a(n) = A121207(2n,n) = A124496(2n,n).
%e A297924 a(1) = 1: 1|2.
%e A297924 a(2) = 4: 12|34, 13|24, 14|23, 1|2|34.
%e A297924 a(3) = 20: 123|456, 124|356, 125|346, 126|345, 12|3|456, 134|256, 135|246, 136|245, 13|2|456, 145|236, 146|235, 156|234, 1|23|456, 14|2|356, 1|24|356, 15|2|346, 1|25|346, 16|2|345, 1|26|345, 1|2|3|456.
%p A297924 b:= proc(n, k) option remember; `if`(n=k, 1,
%p A297924       add(b(n-j, k)*binomial(n-1, j-1), j=1..n-k))
%p A297924     end:
%p A297924 a:= n-> b(2*n, n):
%p A297924 seq(a(n), n=0..25);
%t A297924 b[n_, k_] := b[n, k] = If[n == k, 1, Sum[b[n - j, k]*Binomial[n - 1, j - 1], {j, 1, n - k}]];
%t A297924 a[n_] := b[2*n, n];
%t A297924 Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, May 20 2018, translated from Maple *)
%Y A297924 Cf. A121207, A124496, A276961, A297926.
%K A297924 nonn
%O A297924 0,3
%A A297924 _Alois P. Heinz_, Jan 08 2018