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A288791 Number of blocks of size >= nine in all set partitions of n. 2
1, 11, 122, 1245, 12325, 121136, 1195147, 11915997, 120572790, 1241499241, 13030331671, 139549798524, 1525923634907, 17041290249637, 194394900237176, 2264977282222371, 26951265841776186, 327445918493429897, 4060993235341162405, 51396034231430455550 (list; graph; refs; listen; history; text; internal format)
OFFSET

9,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 9..575

Wikipedia, Partition of a set

FORMULA

a(n) = Bell(n+1) - Sum_{j=0..8} binomial(n,j) * Bell(n-j).

a(n) = Sum_{j=0..n-9} binomial(n,j) * Bell(j).

E.g.f.: (exp(x) - Sum_{k=0..8} 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, 9):

seq(a(n), n=9..30);

MATHEMATICA

Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 9}], {n, 9, 30}] (* Indranil Ghosh, Jul 06 2017 *)

PROG

(Python)

from sympy import bell, binomial

def a(n): return sum([binomial(n, j)*bell(j) for j in range(n - 8)])

print([a(n) for n in range(9, 31)]) # Indranil Ghosh, Jul 06 2017

CROSSREFS

Column k=9 of A283424.

Cf. A000110.

Sequence in context: A176595 A067218 A293805 * A049666 A163462 A334000

Adjacent sequences:  A288788 A288789 A288790 * A288792 A288793 A288794

KEYWORD

nonn,changed

AUTHOR

Alois P. Heinz, Jun 15 2017

STATUS

approved

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Last modified July 5 18:33 EDT 2022. Contains 355101 sequences. (Running on oeis4.)