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

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A213048 Number of preferential arrangements of n labeled elements with repetitions allowed. 1
1, 1, 5, 31, 229, 1981, 19775, 224589, 2864901, 40591255, 632760105, 10765616885, 198543617119, 3945765358653, 84070841065937, 1911864488674531, 46222718892288645, 1183919151676806177, 32025836905529003471, 912372909851608715945, 27304698509111141688969 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

a(n) = Sum_{k=1..n} C(n+k-1,k)*a(n-k) for n>0, a(0) = 1.

a(n) = Sum_c(n) C(n+k1-1,k1) C(n-k1+k2-1,k2) C(n-k1-k2+k3-1,k3) ..., where Sum_c(n) denotes the sum over all compositions (ordered partitions) of n = k1 + k2 + ... .

a(n) ~ c * n! * n^(log(2)) / (log(2))^n, where c = 0.9387523255426859866752735339706007723805611... . - Vaclav Kotesovec, May 03 2015

EXAMPLE

For n=2 the a(2) = 5 solutions are (1,2), (1|2), (2|1), (1|1), (2|2).

MAPLE

a:= proc(n) option remember;

      `if`(n=0, 1, add(binomial(n+k-1, k)*a(n-k), k=1..n))

    end:

seq(a(n), n=0..25);

MATHEMATICA

a[n_] := a[n] = If[n==0, 1, Sum[Binomial[n+k-1, k] a[n-k], {k, 1, n}]];

a /@ Range[0, 25] (* Jean-Fran├žois Alcover, Nov 21 2020 *)

CROSSREFS

Cf. A000670.

Sequence in context: A001910 A052773 A062147 * A069321 A211179 A177797

Adjacent sequences:  A213045 A213046 A213047 * A213049 A213050 A213051

KEYWORD

nonn,changed

AUTHOR

Thomas Wieder, Jun 03 2012

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 November 28 11:28 EST 2020. Contains 338720 sequences. (Running on oeis4.)