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 A001473 Number of degree-n permutations of order exactly 4. (Formerly M4206 N1756) 25
 0, 0, 0, 6, 30, 180, 840, 5460, 30996, 209160, 1290960, 9753480, 69618120, 571627056, 4443697440, 40027718640, 346953934320, 3369416698080, 31421601510336, 328430320909920, 3331475969159520, 37124416523261760 (list; graph; refs; listen; history; text; internal format)
 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:=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

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Last modified September 28 03:41 EDT 2023. Contains 365715 sequences. (Running on oeis4.)