A103620 Number of permutations of n elements admitting a fourth root.

1, 1, 1, 3, 9, 45, 225, 1575, 11130, 100170, 897750, 9875250, 108523800, 1410809400, 18332414100, 274986211500, 4127136413400, 70161319027800, 1192076391706200, 22649451442417800, 430247983427262000, 9035207651972502000

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..250

H. S. Wilf, Generatingfunctionology, 2nd edn., Academic Press, NY, 1994, p. 149, Eq. 4.8.2.

Formula

E.g.f.: ((1+x)/(1-x))^(1/2)*Product(1/2*cos(1/2*x^(2*m)/m)+1/2*cosh(1/2*x^(2*m)/m), m = 1 .. infinity).

Maple

with(combinat): with(numtheory): with(padic):
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      `if`(irem(j, mul(p^ordp(4, p), p=factorset(i)))=0, (i-1)!^j*
      multinomial(n, n-i*j, i$j)/j!*b(n-i*j, i-1), 0), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..25);  # Alois P. Heinz, Sep 09 2014

Mathematica

CoefficientList[Series[((1+x)/(1-x))^(1/2) * Product[1/2*Cos[1/2*x^(2*m)/m] + 1/2*Cosh[1/2*x^(2*m)/m], {m, 1, 20}], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Sep 13 2014 *)

Crossrefs

Cf. A003483, A103619, A102687, A215716, A215717, A215718.

Column k=4 of A247005.

Sequence in context: A262135 A000246 A247006 * A138315 A337849 A328267

Adjacent sequences: A103617 A103618 A103619 * A103621 A103622 A103623

Keyword

nonn

Author

Vladeta Jovovic, Feb 11 2005

Status

approved