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

1, 7, 56, 497, 4809, 50134, 558215, 6593839, 82187658, 1076193867, 14749823893, 210926792244, 3138696242941, 48485723853763, 775929767223352, 12840232627455485, 219355194338036309, 3862794707291567670

Offset: 0

Author

Philippe Deléham, Sep 16 2008

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)

Sage

expnums(18, 7) # Zerinvary Lajos, May 15 2009

Formula

a(n) = Sum_{k=0..n} 7^k*A048993(n,k); A048993: Stirling2 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 shifted 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

G.f.: Sum_{j>=0} 7^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 11 2019

Extensions

More terms from Alois P. Heinz, Oct 09 2008