OFFSET
0,2
COMMENTS
a(n) is also the exp transform ofA010727.-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
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
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
KEYWORD
nonn
AUTHOR
Philippe Deléham,Sep 16 2008
EXTENSIONS
More terms fromAlois P. Heinz,Oct 09 2008
STATUS
approved