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A288788 Number of blocks of size >= 6 in all set partitions of n. 2
1, 8, 65, 502, 3851, 29921, 237426, 1932529, 16173029, 139320277, 1235847277, 11288120480, 106132359679, 1026681599731, 10212591089574, 104393925768077, 1095895294558168, 11806719056706773, 130457490607638988, 1477428802636263486, 17138268233851671782 (list; graph; refs; listen; history; text; internal format)
OFFSET

6,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 6..575

Wikipedia, Partition of a set

FORMULA

a(n) = Bell(n+1) - Sum_{j=0..5} binomial(n,j) * Bell(n-j).

a(n) = Sum_{j=0..n-6} binomial(n,j) * Bell(j).

E.g.f.: (exp(x) - Sum_{k=0..5} x^k/k!) * exp(exp(x) - 1). - Ilya Gutkovskiy, Jun 26 2022

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, 6):

seq(a(n), n=6..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, 6];

Table[a[n], {n, 6, 30}] (* Jean-Fran├žois Alcover, May 28 2018, from Maple *)

CROSSREFS

Column k=6 of A283424.

Cf. A000110.

Sequence in context: A293802 A316872 A317600 * A033118 A033126 A022039

Adjacent sequences:  A288785 A288786 A288787 * A288789 A288790 A288791

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2017

STATUS

approved

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Last modified August 11 07:36 EDT 2022. Contains 356055 sequences. (Running on oeis4.)