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%I #10 Jul 23 2021 03:20:34
%S 1,2,3,8,18,42,102,248,611,1525,3845,9787,25118,64944,169047,442727,
%T 1165990,3086692,8210400,21936230,58851484,158502600,428446818,
%U 1162110731,3162318827,8631705612,23629386708,64865101678,178531867765,492622401009,1362567996602,3777490059587,10495626146222,29223682273897,81535625627546,227935763726546,638409001899851
%N a(n) = floor(bell(2n)/bell(n)^2), bell = A000110.
%C a(n) is the largest integer smaller than the (reciprocal) proportion of partitions of the set {1,..,2n} that refine the partition {1,..,n|n+1,..,2*n}.
%t Table[Floor[BellB[2*n]/BellB[n]^2], {n,0,30}] (* _Vaclav Kotesovec_, Jul 23 2021 *)
%o (GAP) QuoInt(Bell(2*n),Bell(n)^2)
%Y Cf. A000110.
%K nonn
%O 0,2
%A _Nick Loughlin_, May 01 2014
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