login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A144263 Number of ways of placing n labeled balls into n unlabeled (but7-colored) boxes. 15
1, 7, 56, 497, 4809, 50134, 558215, 6593839, 82187658, 1076193867, 14749823893, 210926792244, 3138696242941, 48485723853763, 775929767223352, 12840232627455485, 219355194338036309, 3862794707291567670 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is also the exp transform of A010727. - Alois P. Heinz, Oct 09 2008
The number of ways of putting n labeled balls into a set of bags and then putting the bags into 7 labeled boxes. - Peter Bala, Mar 23 2013
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=0..n} 7^k*A048993(n,k); A048993: Stirling2 numbers.
E.g.f.: exp(7*(exp(x)-1)).
G.f.: 7*(x/(1-x))*A(x/(1-x))= A(x)-1; seven times the binomial transform equals this sequence shifted one place left.
a(n) ~ n^n * exp(n/LambertW(n/7)-7-n) / (sqrt(1+LambertW(n/7)) * LambertW(n/7)^n). - Vaclav Kotesovec, Mar 12 2014
G.f.: Sum_{j>=0} 7^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 11 2019
MAPLE
a:= proc(n) option remember; `if`(n=0, 1,
(1+add(binomial(n-1, k-1)*a(n-k), k=1..n-1))*7)
end:
seq(a(n), n=0..25); # Alois P. Heinz, Oct 09 2008
MATHEMATICA
Table[BellB[n, 7], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *)
PROG
(Sage) expnums(18, 7) # Zerinvary Lajos, May 15 2009
CROSSREFS
Sequence in context: A265233 A165322 A082305 * A001730 A259900 A087751
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 16 2008
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)