A275310 Number of set partitions of [n] with nonincreasing block sizes.

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

Offset: 0

Author

Alois P. Heinz, Jul 22 2016

Keywords

• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..612
• Wikipedia, Partition of a set

Crossrefs

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

Programs

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-François Alcover, Feb 02 2017, translated from Maple *)