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A144223 Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes. 13
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: Stirling-2 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

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 * A262671 A029588 A001725

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

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Last modified February 23 07:06 EST 2018. Contains 299473 sequences. (Running on oeis4.)