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!)
A262320 Number of ways to select a subset s from an n-set and then partition s into blocks of equal size. 4
1, 2, 5, 12, 30, 73, 191, 528, 1553, 5032, 18088, 66905, 266382, 1164517, 5215645, 23868104, 117740144, 609872351, 3268548407, 18110463456, 102867877415, 620476915966, 4005216028162, 25747549921339, 166978155172421, 1168774024335204, 8556355097320142 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..616

FORMULA

E.g.f.: exp(x) * (1 + Sum_{k>=1} (exp(x^k/k!)-1)).

a(n) = 1 + Sum_{k=1..n} C(n,k) * A038041(k).

a(n) = 1 + A262280(n).

a(n) = Sum_{k=0..n} A262321(k).

EXAMPLE

a(3) = 12: {}, 1, 2, 3, 12, 1|2, 13, 1|3, 23, 2|3, 123, 1|2|3.

MAPLE

b:= proc(n) option remember;

      add(1/(d!*(n/d)!^d), d=numtheory[divisors](n))

    end:

a:= n-> 1 + n! * add(b(k)/(n-k)!, k=1..n):

seq(a(n), n=0..30);

MATHEMATICA

b[n_] := b[n] = DivisorSum[n, 1/(#!*(n/#)!^#)&]; a[n_] := 1 + n! * Sum[b[k]/(n-k)!, {k, 1, n}]; Table[a[n], {n, 0, 30}] (* Jean-Fran├žois Alcover, Dec 18 2016, after Alois P. Heinz *)

CROSSREFS

Partial sums of A262321.

Cf. A038041, A262280.

Sequence in context: A052109 A157748 A046170 * A062423 A118649 A033482

Adjacent sequences:  A262317 A262318 A262319 * A262321 A262322 A262323

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2015

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 July 5 00:01 EDT 2020. Contains 335457 sequences. (Running on oeis4.)