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A144223 Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes. 15
1, 6, 42, 330, 2850, 26682, 268098, 2869242, 32510850, 388109562, 4861622850, 63682081530, 869725707522, 12352785293562, 182049635623362, 2778394592545530, 43833623157604482, 713738052924821754 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n) is also the exp transform of A010722. - 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 6 labeled boxes. - Peter Bala, Mar 23 2013
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = Sum_{k=0..n} 6^k*A048993(n,k); A048993: Stirling2 numbers.
G.f.: 6*(x/(1-x))*A(x/(1-x)) = A(x)-1; six times the binomial transform equals this sequence shifted one place left.
E.g.f.: exp(6(e^x-1)).
G.f.: T(0)/(1-6*x), where T(k) = 1 - 6*x^2*(k+1)/(6*x^2*(k+1) - (1-6*x-x*k)*(1-7*x-x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 04 2013
a(n) ~ n^n * exp(n/LambertW(n/6)-6-n) / (sqrt(1+LambertW(n/6)) * LambertW(n/6)^n). - Vaclav Kotesovec, Mar 12 2014
G.f.: Sum_{j>=0} 6^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 07 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))*6)
end:
seq(a(n), n=0..25); # Alois P. Heinz, Oct 09 2008
MATHEMATICA
Table[BellB[n, 6], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *)
PROG
(Sage) expnums(18, 6) # Zerinvary Lajos, May 15 2009
CROSSREFS
Sequence in context: A218755 A165314 A082302 * A320758 A367241 A262671
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 14 2008
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved

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