A275311 Number of set partitions of [n] with nondecreasing block sizes.

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

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-François Alcover, Jan 22 2017, translated from Maple *)

Crossrefs

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

Sequence in context: A035003 A143879 A056293 * A056294 A084423 A361910

Adjacent sequences: A275308 A275309 A275310 * A275312 A275313 A275314

Keyword

nonn

Author

Alois P. Heinz, Jul 22 2016

Status

approved