|
|
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
|
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
|
|
|
FORMULA
|
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:
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|