login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A288790 Number of blocks of size >= eight in all set partitions of n. 2
1, 10, 101, 947, 8670, 79249, 730745, 6838642, 65197797, 634656360, 6316333291, 64318009411, 670336612614, 7151290120037, 78085166445577, 872478836270306, 9972817907218608, 116575837400037486, 1393037460835481622, 17010118386233081680, 212160149063581345610 (list; graph; refs; listen; history; text; internal format)
OFFSET

8,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 8..575

Wikipedia, Partition of a set

FORMULA

a(n) = Bell(n+1) - Sum_{j=0..7} binomial(n,j) * Bell(n-j).

a(n) = Sum_{j=0..n-8} 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, 8):

seq(a(n), n=8..30);

MATHEMATICA

Table[Sum[Binomial[n, j] BellB[j], {j, 0, n - 8}], {n, 8, 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 - 7)])

print [a(n) for n in range(8, 31)] # Indranil Ghosh, Jul 06 2017

CROSSREFS

Column k=8 of A283424.

Cf. A000110.

Sequence in context: A214390 A293804 A210167 * A280371 A105032 A281102

Adjacent sequences:  A288787 A288788 A288789 * A288791 A288792 A288793

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 15 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 22:25 EDT 2020. Contains 337174 sequences. (Running on oeis4.)