A241906 a(n) = floor(bell(2n)/bell(n)^2), bell = A000110.

1, 2, 3, 8, 18, 42, 102, 248, 611, 1525, 3845, 9787, 25118, 64944, 169047, 442727, 1165990, 3086692, 8210400, 21936230, 58851484, 158502600, 428446818, 1162110731, 3162318827, 8631705612, 23629386708, 64865101678, 178531867765, 492622401009, 1362567996602, 3777490059587, 10495626146222, 29223682273897, 81535625627546, 227935763726546, 638409001899851

Offset: 0

Author

Nick Loughlin, May 01 2014

Keywords

• nonn

Comments

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}.

Crossrefs

Cf. A000110.

Programs

GAP

QuoInt(Bell(2*n),Bell(n)^2)

Mathematica

Table[Floor[BellB[2*n]/BellB[n]^2], {n,0,30}] (* Vaclav Kotesovec, Jul 23 2021 *)