A001473 Number of degree-n permutations of order exactly 4. (Formerly M4206 N1756)

0, 0, 0, 6, 30, 180, 840, 5460, 30996, 209160, 1290960, 9753480, 69618120, 571627056, 4443697440, 40027718640, 346953934320, 3369416698080, 31421601510336, 328430320909920, 3331475969159520, 37124416523261760

Offset

1,4

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

G. C. Greubel, Table of n, a(n) for n = 1..565

L. Moser and M. Wyman, On solutions of x^d = 1 in symmetric groups, Canad. J. Math., 7 (1955), 159-168.

Formula

E.g.f.: exp(x + x^2/2 + x^4/4) - exp(x + x^2/2).

Mathematica

Rest@With[{m = 30}, CoefficientList[Series[Exp[x +x^2/2 +x^4/4] - Exp[x +x^2/2], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, May 14 2019 *)

Prog

(PARI) my(x=xx+O(xx^33)); concat([0, 0, 0], Vec(serlaplace(-exp(x+1/2*x^2) +exp(x+1/2*x^2+1/4*x^4)))) \\ Michel Marcus, Dec 12 2014
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^2/2 +x^4/4) -Exp(x+x^2/2) )); [0, 0, 0] cat [Factorial(n+3)*b[n]: n in [1..m-4]]; // G. C. Greubel, May 14 2019
(Sage) m = 30; T = taylor(exp(x +x^2/2 +x^4/4) - exp(x+x^2/2), x, 0, m); a=[factorial(n)*T.coefficient(x, n) for n in (0..m)]; a[1:] # G. C. Greubel, May 14 2019

Crossrefs

Cf. A000085, A001470, A001472, A052501, A053496-A053505, A001189, A001471, A001473, A061121-A061128.

Column k=4 of A057731.

Sequence in context: A001341 A089896 A057754 * A334288 A063888 A029571

Adjacent sequences: A001470 A001471 A001472 * A001474 A001475 A001476

Keyword

nonn

Author

N. J. A. Sloane and J. H. Conway

Extensions

More terms from Vladeta Jovovic, Apr 14 2001

Status

approved