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A275310 Number of set partitions of [n] with nonincreasing block sizes. 8
1, 1, 2, 4, 11, 30, 102, 346, 1353, 5444, 24170, 110082, 546075, 2777828, 15099359, 84491723, 499665713, 3035284304, 19375261490, 126821116410, 866293979945, 6072753348997, 44193947169228, 329387416656794, 2542173092336648, 20069525888319293 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..612

Wikipedia, Partition of a set

EXAMPLE

a(3) = 4: 123, 12|3, 13|2, 1|2|3.

a(4) = 11: 1234, 123|4, 124|3, 12|34, 12|3|4, 134|2, 13|24, 13|2|4, 14|23, 14|2|3, 1|2|3|4.

MAPLE

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

      b(n-j, j)*binomial(n-1, j-1), j=1..min(n, i)))

    end:

a:= n-> b(n$2):

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

MATHEMATICA

b[n_, i_] := b[n, i] = If[n==0, 1, Sum[b[n-j, j]*Binomial[n-1, j-1], {j, 1, Min[n, i]}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Feb 02 2017, translated from Maple *)

CROSSREFS

Cf. A007837, A038041, A275309, A275311, A275312, A275313, A286071.

Sequence in context: A339225 A148158 A148159 * A102814 A193059 A034770

Adjacent sequences:  A275307 A275308 A275309 * A275311 A275312 A275313

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 22 2016

STATUS

approved

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Last modified June 15 00:00 EDT 2021. Contains 345041 sequences. (Running on oeis4.)