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!)
A144223 Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes. 14
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

Alois P. Heinz, Table of n, a(n) for n = 0..200

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

Cf. A000110, A001861, A027710, A078944, A144180. A144263, A189233, A221159, A221176.

Sequence in context: A218755 A165314 A082302 * A320758 A262671 A029588

Adjacent sequences:  A144220 A144221 A144222 * A144224 A144225 A144226

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 14 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 24 01:40 EST 2020. Contains 338603 sequences. (Running on oeis4.)