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A229228 Number of set partitions of {1,...,2n} into sets of size at most n.

%I A229228 #16 May 21 2018 15:22:36
%S A229228 1,1,10,166,3795,112124,4163743,190168577,10468226150,681863474058,
%T A229228 51720008131148,4506628734688128,445956917001833090,
%U A229228 49631199898024188422,6160538225093750695800,846748983034696433927334,128064669166890886264698699,21195039362681903376709497444
%N A229228 Number of set partitions of {1,...,2n} into sets of size at most n.
%H A229228 Alois P. Heinz, <a href="/A229228/b229228.txt">Table of n, a(n) for n = 0..200</a>
%F A229228 a(n) = (2n)! * [x^(2n)] exp(Sum_{j=1..n} x^j/j!).
%F A229228 a(n) = A229223(2n,n).
%e A229228 a(2) = 10: 1/2/3/4, 12/3/4, 13/2/4, 14/2/3, 1/23/4, 1/24/3, 1/2/34, 12/34, 13/24, 14/23.
%p A229228 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229228       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229228       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229228     end:
%p A229228 a:= n-> G(2*n, n):
%p A229228 seq(a(n), n=0..20);
%t A229228 G[n_, k_] := G[n, k] = If[n == 0, 1, If[k < 1, 0, Sum[G[n - k*j, k - 1]*n!/ k!^j/(n - k*j)!/j!, {j, 0, n/k}]]];
%t A229228 Table[G[2n, n], {n, 0, 20}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)
%Y A229228 Column k=2 of A229243.
%Y A229228 Cf. A229223.
%K A229228 nonn
%O A229228 0,3
%A A229228 _Alois P. Heinz_, Sep 16 2013