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A275311 Number of set partitions of [n] with nondecreasing block sizes. 8
1, 1, 2, 3, 7, 12, 43, 89, 363, 1096, 4349, 14575, 77166, 265648, 1369284, 6700177, 33526541, 162825946, 1034556673, 5157939218, 33054650345, 206612195885, 1244742654646, 8071979804457, 62003987375957, 381323590616995, 2827411772791596, 22061592185044910 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..617

Wikipedia, Partition of a set

EXAMPLE

a(3) = 3: 123, 1|23, 1|2|3.

a(4) = 7: 1234, 12|34, 13|24, 14|23, 1|234, 1|2|34, 1|2|3|4.

a(5) = 12: 12345, 12|345, 13|245, 14|235, 15|234, 1|2345, 1|23|45, 1|24|35, 1|25|34, 1|2|345, 1|2|3|45, 1|2|3|4|5.

MAPLE

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

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

    end:

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

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, i, n}]]; a[n_] := b[n, 1]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Jan 22 2017, translated from Maple *)

CROSSREFS

Cf. A007837, A038041, A275309, A275310, A275312, A275313, A286074.

Sequence in context: A035003 A143879 A056293 * A056294 A084423 A068134

Adjacent sequences:  A275308 A275309 A275310 * A275312 A275313 A275314

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 22 2016

STATUS

approved

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)