OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..578
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 139.
FORMULA
E.g.f.: Sum_{k>=1} Integral of x^(k-1)/(k-1)! * exp(exp(x) - Sum_{i=0..k} x^i/i!) dx.
EXAMPLE
a(5) = 9 because we have: {{1,2,3,4,5}}, {{1},{2,3,4,5}}, {{1,2},{3,4,5}}, {{1,3},{2,4,5}}, {{1,5},{2,3,4}}, {{1,4},{2,3,5}}, {{1},{2,3},{4,5}}, {{1},{2,5},{3,4}}, {{1},{2,4},{3,5}}.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, add(
binomial(n-1, i-1)*b(n-i, `if`(t=1, i+1, t)), i=t..n))
end:
a:= n-> `if`(n=0, 0, b(n, 1)):
seq(a(n), n=1..30); # Alois P. Heinz, Jul 07 2016
MATHEMATICA
nn=20; Drop[Range[0, nn]!CoefficientList[Series[Sum[Integrate[x^(k-1)/(k-1)! Exp[Exp[x]-Sum[x^i/i!, {i, 0, k}]], x], {k, 1, nn}], {x, 0, nn}], x], 1]
(* Second program: *)
b[n_, t_] := b[n, t] = If[n==0, 1, Sum[Binomial[n-1, i-1]*b[n-i, If[t==1, i + 1, t]], {i, t, n}]]; a[n_] := If[n==0, 0, b[n, 1]]; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 08 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 01 2013
STATUS
approved