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
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014
N. J. A. Sloane, Transforms
FORMULA
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
G.f.: Sum_{j>=0} 5^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))*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
KEYWORD
nonn
AUTHOR
Philippe Deléham, Sep 12 2008
EXTENSIONS
More terms from Alois P. Heinz, Oct 09 2008
STATUS
approved