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A287666 Number of set partitions of [n] such that j is member of block b only if b = 1 or at least one of j-1, ..., j-3 is member of a block >= b-1. 2
1, 1, 2, 5, 15, 52, 202, 861, 3970, 19596, 102703, 567867, 3295439, 19986462, 126231946, 827759525, 5621051650, 39439867696, 285368007479, 2125566382124, 16273261632111, 127881070062521, 1030221084660031, 8498826714433335, 71721238761675612, 618573094313147709 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..150

Wikipedia, Partition of a set

FORMULA

a(n) = A287641(n,3).

a(n) = A000110(n) for n <= 5.

EXAMPLE

a(6) = 202 = 203 - 1 = A000110(6) - 1 counts all set partitions of [6] except: 1345|2|6.

MAPLE

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

      [seq(max(l[i], j), i=2..nops(l)), j]), j=1..l[1]+1))

    end:

a:= n-> b(n, [0$3]):

seq(a(n), n=0..26);

MATHEMATICA

b[n_, l_] := b[n, l] = If[n == 0, 1, Sum[b[n - 1, Append[Table[Max[l[[i]], j], {i, 2, Length[l]}], j]], {j, 1, l[[1]] + 1}]];

a[n_] := b[n, {0, 0, 0}];

Table[a[n], {n, 0, 26}] (* Jean-Fran├žois Alcover, May 27 2018, from Maple *)

CROSSREFS

Column k=3 of A287641.

Cf. A000110.

Sequence in context: A220912 A108304 A220913 * A158829 A306551 A110038

Adjacent sequences:  A287663 A287664 A287665 * A287667 A287668 A287669

KEYWORD

nonn

AUTHOR

Alois P. Heinz, May 29 2017

STATUS

approved

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Last modified October 19 03:24 EDT 2019. Contains 328211 sequences. (Running on oeis4.)