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A288786 Number of blocks of size >= four in all set partitions of n. 2
1, 6, 37, 225, 1395, 8944, 59585, 413117, 2981310, 22380814, 174600298, 1413841252, 11868587577, 103155618776, 927141821215, 8606806236367, 82430269073469, 813600584094320, 8267450613029789, 86406853732930699, 927993270700444588, 10232636504064477996 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..575

Wikipedia, Partition of a set

FORMULA

a(n) = Bell(n+1) - Sum_{j=0..3} binomial(n,j) * Bell(n-j).

a(n) = Sum_{j=0..n-4} binomial(n,j) * Bell(j).

MAPLE

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

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

    end:

g:= proc(n, k) option remember; `if`(n<k, 0,

      g(n, k+1) +binomial(n, k)*b(n-k))

    end:

a:= n-> g(n, 4):

seq(a(n), n=4..30);

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1, Sum[b[n - j]*Binomial[n-1, j-1], {j, 1, n}]];

g[n_, k_] := g[n, k] = If[n < k, 0, g[n, k+1] + Binomial[n, k]*b[n - k]];

a[n_] := g[n, 4];

Table[a[n], {n, 4, 30}] (* Jean-Fran├žois Alcover, May 28 2018, from Maple *)

CROSSREFS

Column k=4 of A283424.

Cf. A000110.

Sequence in context: A244618 A033116 A033124 * A180032 A022035 A255119

Adjacent sequences:  A288783 A288784 A288785 * A288787 A288788 A288789

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2017

STATUS

approved

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Last modified February 23 00:28 EST 2020. Contains 332157 sequences. (Running on oeis4.)