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A292347
Möbius function of absolute order.
1
1, 0, 2, 16, 192, 3008, 58480, 1360896, 36931328, 1145967616, 40040976384, 1556236513280, 66610814414848, 3113899625938944, 157874306413611008, 8629070019375726592, 505841319779582607360, 31659277087340088786944, 2107162955059322401718272
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
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
Sequence in context: A183205 A006335 A273591 * A051711 A274448 A209586
KEYWORD
nonn
AUTHOR
Richard Stanley, Dec 07 2017
STATUS
approved