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A241906
a(n) = floor(bell(2n)/bell(n)^2), bell = A000110.
0
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
0,2
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}.
MATHEMATICA
Table[Floor[BellB[2*n]/BellB[n]^2], {n, 0, 30}] (* Vaclav Kotesovec, Jul 23 2021 *)
PROG
(GAP) QuoInt(Bell(2*n), Bell(n)^2)
CROSSREFS
Cf. A000110.
Sequence in context: A034066 A034076 A272642 * A079224 A002369 A005957
KEYWORD
nonn
AUTHOR
Nick Loughlin, May 01 2014
STATUS
approved