OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..444
FORMULA
E.g.f.: Sum_{k>0} (exp(x^k/(1-x))-1).
EXAMPLE
For n=4 we have 73 sets of lists (cf. A000262): (1234) (24 ways), (123)(4) (6*4 ways), (12)(34) (3*4 ways), (12)(3)(4) (6*2 ways), (1)(2)(3)(4) (1 way); so a(n)= 24*4+24*1+12*2+12*1+1*1 = 157.
MAPLE
b:= proc(n, m) option remember; `if`(n=0, m, add(j!*
b(n-j, min(m, j))*binomial(n-1, j-1), j=1..n))
end:
a:= n-> `if`(n=0, 0, b(n, infinity)):
seq(a(n), n=0..25); # Alois P. Heinz, May 10 2016
MATHEMATICA
b[n_, m_] := b[n, m] = If[n==0, m, Sum[j!*b[n-j, Min[m, j]]*Binomial[n-1, j - 1], {j, 1, n}]]; a[n_] := If[n==0, 0, b[n, Infinity]]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 18 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jul 27 2004
EXTENSIONS
More terms from Max Alekseyev, Jul 04 2009
a(0)=0 prepended by Alois P. Heinz, May 10 2016
STATUS
approved