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A288792 Number of blocks of size >= ten in all set partitions of n. 2
1, 12, 145, 1600, 17032, 179132, 1883117, 19929390, 213332101, 2316793121, 25577181324, 287421068697, 3290394397097, 38393883291996, 456753452800691, 5540597439008861, 68530489547341697, 864218608315007230, 11109867095322262250, 145563654356205885737 (list; graph; refs; listen; history; text; internal format)
OFFSET

10,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 10..576

Wikipedia, Partition of a set

FORMULA

a(n) = Bell(n+1) - Sum_{j=0..9} binomial(n,j) * Bell(n-j).

a(n) = Sum_{j=0..n-10} 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, 10):

seq(a(n), n=10..30);

MATHEMATICA

Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 10}], {n, 10, 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 - 9)])

print([a(n) for n in range(10, 31)]) # Indranil Ghosh, Jul 06 2017

CROSSREFS

Column k=10 of A283424.

Cf. A000110.

Sequence in context: A067219 A075619 A055332 * A041061 A174227 A041266

Adjacent sequences:  A288789 A288790 A288791 * A288793 A288794 A288795

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2017

STATUS

approved

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Last modified May 26 13:59 EDT 2022. Contains 354092 sequences. (Running on oeis4.)