OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..444
FORMULA
E.g.f.: exp(x/(1-x))*Sum_{k>0} (1-exp(x^k/(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(4)= 24*4+24*3+12*2+12*2+1*1 = 217.
MAPLE
b:= proc(n, m) option remember; `if`(n=0, m, add(j!*
b(n-j, max(m, j))*binomial(n-1, j-1), j=1..n))
end:
a:= n-> b(n, 0):
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, Max[m, j]] Binomial[n-1, j-1], {j, 1, n}]];
a[n_] := b[n, 0];
a /@ Range[0, 25] (* Jean-François Alcover, Nov 05 2020, after Alois P. Heinz *)
PROG
(PARI)
N=50; x='x+O('x^N);
egf=exp(x/(1-x))*sum(k=1, N, (1-exp(x^k/(x-1))) );
Vec( serlaplace(egf) ) /* show terms */
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Jul 27 2004
EXTENSIONS
a(0)=0 prepended by Alois P. Heinz, May 10 2016
STATUS
approved