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A275312 Number of set partitions of [n] with increasing block sizes. 8
1, 1, 1, 2, 2, 6, 11, 28, 51, 242, 532, 1545, 6188, 16592, 86940, 302909, 967523, 3808673, 23029861, 71772352, 484629531, 1840886853, 9376324526, 37878035106, 204542429832, 1458360522892, 6241489795503, 45783932444672, 211848342780210, 1137580874772724 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..728

Wikipedia, Partition of a set

EXAMPLE

a(4) = 2: 1234, 1|234.

a(5) = 6: 12345, 12|345, 13|245, 14|235, 15|234, 1|2345.

a(6) = 11: 123456, 12|3456, 13|2456, 14|2356, 15|2346, 16|2345, 1|23456, 1|23|456, 1|24|356, 1|25|346, 1|26|345.

MAPLE

b:= proc(n, i) option remember; `if`(n=0, 1,

     `if`(i>n, 0, b(n, i+1)+b(n-i, i+1)*binomial(n-1, i-1)))

    end:

a:= n-> b(n, 1):

seq(a(n), n=0..35);

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i+1] + b[n-i, i+1] * Binomial[n-1, i-1]]]; a[n_] := b[n, 1]; Table[a[n], {n, 0, 35}] (* Jean-François Alcover, Jan 22 2017, translated from Maple *)

CROSSREFS

Cf. A007837, A038041, A275309, A275310, A275311, A275313, A286075.

Sequence in context: A279212 A299018 A269830 * A209026 A091764 A335311

Adjacent sequences:  A275309 A275310 A275311 * A275313 A275314 A275315

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 22 2016

STATUS

approved

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Last modified July 26 13:40 EDT 2021. Contains 346294 sequences. (Running on oeis4.)