A292347 Möbius function of absolute order.

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

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

Cf. A000108, A008683.

Sequence in context: A183205 A006335 A273591 * A051711 A274448 A209586

Adjacent sequences: A292344 A292345 A292346 * A292348 A292349 A292350

Keyword

nonn

Author

Richard Stanley, Dec 07 2017

Status

approved