OFFSET
0,5
COMMENTS
a(n) = A186754(n,0).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..450
FORMULA
E.g.f.: exp(1-exp(z))/(1-z).
a(n) ~ n! * exp(1-exp(1)) = 0.179374... * n!. - Vaclav Kotesovec, Mar 17 2014
EXAMPLE
a(4)=5 because we have (1432), (1342), (1423), (1243), and (1324).
a(5)=23 counts all cyclic permutations of {1,2,3,4,5}, except (12345).
MAPLE
g := exp(1-exp(z))/(1-z): gser := series(g, z = 0, 25): seq(factorial(n)*coeff(gser, z, n), n = 0 .. 22);
# second Maple program:
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-j)*binomial(n-1, j-1)*((j-1)!-1), j=1..n))
end:
seq(a(n), n=0..25); # Alois P. Heinz, Apr 13 2017
MATHEMATICA
With[{nn=30}, CoefficientList[Series[Exp[1-Exp[x]]/(1-x), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 23 2016 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Feb 26 2011
STATUS
approved