OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..450
FORMULA
E.g.f.: Sum_{k>=1} Integral_((x^(k-1)/(k-1))*exp(-Sum_{i=1..k} x^i/i)/(1-x) dx).
EXAMPLE
a(4) = 8 because we have the permutations of {1,2,3,4} in cycle notation:
{{1}, {3,4,2}}, {{1}, {4,3,2}}, {{2,3,4,1}}, {{2,4,3,1}}, {{3,4,2,1}}, {{3,2,4,1}}, {{4,3,2,1}}, {{4,2,3,1}}.
MAPLE
b:= proc(n, t) option remember; `if`(n=0, 1, add((i-1)!*
binomial(n-1, i-1)*b(n-i, `if`(t=1, i+1, t)), i=t..n))
end:
a:= n-> b(n, 1):
seq(a(n), n=1..30); # Alois P. Heinz, Sep 07 2020
MATHEMATICA
nn=20; Drop[Range[0, nn]! CoefficientList[Series[Sum[Integrate[x^(k-1) Exp[-Sum[x^i/i, {i, 1, k}]]/(1-x), x], {k, 1, nn}], {x, 0, nn}], x], 1]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Apr 01 2013
STATUS
approved