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A103620 Number of permutations of n elements admitting a fourth root. 7
1, 1, 1, 3, 9, 45, 225, 1575, 11130, 100170, 897750, 9875250, 108523800, 1410809400, 18332414100, 274986211500, 4127136413400, 70161319027800, 1192076391706200, 22649451442417800, 430247983427262000, 9035207651972502000 (list; graph; refs; listen; history; text; internal format)
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 A328267 A038059

Adjacent sequences:  A103617 A103618 A103619 * A103621 A103622 A103623

KEYWORD

nonn

AUTHOR

Vladeta Jovovic, Feb 11 2005

STATUS

approved

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Last modified June 4 10:04 EDT 2020. Contains 334825 sequences. (Running on oeis4.)