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A144180 Number of ways of placing n labeled balls into n unlabeled (but 5-colored) boxes. 15
1, 5, 30, 205, 1555, 12880, 115155, 1101705, 11202680, 120415755, 1362057155, 16151603830, 200144023805, 2584429030505, 34691478901030, 483040313859705, 6963313750468055, 103747357497925880, 1595132080103893655 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is also the exp transform of A010716. - 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 5 labeled boxes. - Peter Bala, Mar 23 2013

REFERENCES

H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014

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} 5^k * A048993(n,k); A048993: Stirling-2 numbers.

G.f.: A(x) satisfies 5*(x/(1-x))*A(x/(1-x)) = A(x)-1; five times the binomial transform equals this sequence shifted one place left.

E.g.f.: exp(5*(exp(x)-1)).

G.f.: (G(0) - 1)/(x-1)/5 where G(k) =  1 - 5/(1-k*x)/(1-x/(x-1/G(k+1) )); (recursively defined continued fraction). - Sergei N. Gladkovskii, Jan 16 2013

a(n) ~ n^n * exp(n/LambertW(n/5)-5-n) / (sqrt(1+LambertW(n/5)) * LambertW(n/5)^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))*5)

    end:

seq(a(n), n=0..25); # Alois P. Heinz, Oct 09 2008

MATHEMATICA

Table[BellB[n, 5], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *)

PROG

(Sage) expnums(19, 5) # Zerinvary Lajos, May 15 2009

CROSSREFS

Cf. A000110, A001861, A027710, A078944. A144223, A144263, A189233, A221159, A221176.

Sequence in context: A253076 A165312 A082301 * A222050 A091122 A029587

Adjacent sequences:  A144177 A144178 A144179 * A144181 A144182 A144183

KEYWORD

nonn

AUTHOR

Philippe Deléham, Sep 12 2008

EXTENSIONS

More terms from Alois P. Heinz, Oct 09 2008

STATUS

approved

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Last modified October 16 21:57 EDT 2018. Contains 316275 sequences. (Running on oeis4.)