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A144263 Number of ways of placing n labeled balls into n unlabeled (but7-colored) boxes. 13
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

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

N. J. A. Sloane, Transforms

FORMULA

a(n) = Sum_{k=0..n} 7^k*A048993(n,k); A048993: Stirling-2 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 shiftd 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

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

Cf. A000110, A001861, A027710, A078944, A144180, A144223. A189233, A221159, A221176.

Sequence in context: A265233 A165322 A082305 * A001730 A259900 A087751

Adjacent sequences:  A144260 A144261 A144262 * A144264 A144265 A144266

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 16 2008

EXTENSIONS

More terms from Alois P. Heinz, Oct 09 2008

STATUS

approved

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Last modified February 22 15:12 EST 2018. Contains 299454 sequences. (Running on oeis4.)