OFFSET
1,3
COMMENTS
(-1)^{n-1} a(n) is the Möbius function value mu(0,1) of the absolute order on the symmetric group S_n with a top element 1 adjoined.
REFERENCES
R. Stanley, Enumerative Combinatorics, vol. 1, second ed., Cambridge University Press (2012), Exercise 3.159.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..367
FORMULA
The exponential generating function for (-1)^{n-1} a(n) is exp(Sum_{p>=1} C(p-1) * x^p/p) = (-1+sqrt(1+4*x))*exp(-1+sqrt(1+4*x))/(2*x), where C(p-1) is a Catalan number.
MAPLE
a:= n-> n! * abs(coeff(series((sqrt(1+4*x)-1)*
exp(sqrt(1+4*x)-1)/(2*x), x, n+3), x, n)):
seq(a(n), n=1..25); # Alois P. Heinz, Dec 08 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Richard Stanley, Dec 07 2017
STATUS
approved