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A275309 Number of set partitions of [n] with decreasing block sizes. 8
1, 1, 1, 3, 4, 11, 36, 82, 239, 821, 3742, 10328, 42934, 156070, 729249, 4025361, 15032099, 68746675, 334541624, 1645575386, 9104991312, 65010298257, 282768687257, 1616844660914, 8660050947383, 53262316928024, 309119883729116, 2185141720645817 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..717

Wikipedia, Partition of a set

EXAMPLE

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

a(4) = 4: 1234, 123|4, 124|3, 134|2.

a(5) = 11: 12345, 1234|5, 1235|4, 123|45, 1245|3, 124|35, 125|34, 1345|2, 134|25, 135|24, 145|23.

MAPLE

b:= proc(n, i) option remember;

      `if`(n>i*(i+1)/2, 0, `if`(n=0, 1, b(n, i-1)+

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

    end:

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

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

MATHEMATICA

b[n_, i_] := b[n, i] = If[n > i*(i + 1)/2, 0, If[n == 0, 1, b[n, i - 1] +  If[i > n, 0, b[n - i, i - 1]*Binomial[n - 1, i - 1]]]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 35}] (* Jean-Fran├žois Alcover, Jan 21 2017, translated from Maple *)

CROSSREFS

Cf. A007837, A038041, A275310, A275311, A275312, A275313, A286073.

Sequence in context: A038559 A242044 A344263 * A119042 A042273 A179167

Adjacent sequences:  A275306 A275307 A275308 * A275310 A275311 A275312

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jul 22 2016

STATUS

approved

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Last modified June 21 02:05 EDT 2021. Contains 345342 sequences. (Running on oeis4.)