cp's OEIS Frontend

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

%I A144263 #29 Jan 25 2020 18:13:42
%S A144263 1,7,56,497,4809,50134,558215,6593839,82187658,1076193867,14749823893,
%T A144263 210926792244,3138696242941,48485723853763,775929767223352,
%U A144263 12840232627455485,219355194338036309,3862794707291567670
%N A144263 Number of ways of placing n labeled balls into n unlabeled (but7-colored) boxes.
%C A144263 a(n) is also the exp transform of A010727. - _Alois P. Heinz_, Oct 09 2008
%C A144263 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
%H A144263 Alois P. Heinz, <a href="/A144263/b144263.txt">Table of n, a(n) for n = 0..200</a>
%H A144263 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A144263 a(n) = Sum_{k=0..n} 7^k*A048993(n,k); A048993: Stirling2 numbers.
%F A144263 E.g.f.: exp(7*(exp(x)-1)).
%F A144263 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.
%F A144263 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
%F A144263 G.f.: Sum_{j>=0} 7^j*x^j / Product_{k=1..j} (1 - k*x). - _Ilya Gutkovskiy_, Apr 11 2019
%p A144263 a:= proc(n) option remember; `if`(n=0, 1,
%p A144263       (1+add(binomial(n-1, k-1)*a(n-k), k=1..n-1))*7)
%p A144263     end:
%p A144263 seq(a(n), n=0..25); # _Alois P. Heinz_, Oct 09 2008
%t A144263 Table[BellB[n,7],{n,0,20}] (* _Vaclav Kotesovec_, Mar 12 2014 *)
%o A144263 (Sage) expnums(18, 7) # _Zerinvary Lajos_, May 15 2009
%Y A144263 Cf. A000110, A001861, A027710, A078944, A144180, A144223. A189233, A221159, A221176.
%K A144263 nonn
%O A144263 0,2
%A A144263 _Philippe Deléham_, Sep 16 2008
%E A144263 More terms from _Alois P. Heinz_, Oct 09 2008