OFFSET
0,2
COMMENTS
a(n) is also the exp transform of A010722. - 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 6 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
G.f.: 6*(x/(1-x))*A(x/(1-x)) = A(x)-1; six times the binomial transform equals this sequence shifted one place left.
E.g.f.: exp(6(e^x-1)).
G.f.: T(0)/(1-6*x), where T(k) = 1 - 6*x^2*(k+1)/(6*x^2*(k+1) - (1-6*x-x*k)*(1-7*x-x*k)/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Dec 04 2013
a(n) ~ n^n * exp(n/LambertW(n/6)-6-n) / (sqrt(1+LambertW(n/6)) * LambertW(n/6)^n). - Vaclav Kotesovec, Mar 12 2014
G.f.: Sum_{j>=0} 6^j*x^j / Product_{k=1..j} (1 - k*x). - Ilya Gutkovskiy, Apr 07 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))*6)
end:
seq(a(n), n=0..25); # Alois P. Heinz, Oct 09 2008
MATHEMATICA
Table[BellB[n, 6], {n, 0, 20}] (* Vaclav Kotesovec, Mar 12 2014 *)
PROG
(Sage) expnums(18, 6) # Zerinvary Lajos, May 15 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 14 2008
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved