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 A053498 Number of degree-n permutations of order dividing 8. 3
 1, 1, 2, 4, 16, 56, 256, 1072, 11264, 78976, 672256, 4653056, 49810432, 433429504, 4448608256, 39221579776, 607251736576, 7244686764032, 101611422797824, 1170362064019456, 19281174853615616, 261583327556386816, 4084459360167657472, 54366023748591386624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Example 5.2.10. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 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 + x^8/8). MAPLE a:= proc(n) option remember; `if`(n<0, 0, `if`(n=0, 1,        add(mul(n-i, i=1..j-1)*a(n-j), j=[1, 2, 4, 8])))     end: seq(a(n), n=0..25);  # Alois P. Heinz, Feb 14 2013 MATHEMATICA CoefficientList[Series[Exp[x+x^2/2+x^4/4+x^8/8], {x, 0, 23}], x]*Range[0, 23]! (* Jean-François Alcover, Mar 24 2014 *) PROG (PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x +x^2/2 +x^4/4 +x^8/8) )) \\ G. C. Greubel, May 14 2019 (MAGMA) m:=30; R:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x +x^2/2 +x^4/4 +x^8/8) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, May 14 2019 (Sage) m = 30; T = taylor(exp(x +x^2/2 +x^4/4 +x^8/8), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, May 14 2019 CROSSREFS Cf. A000085, A001470, A001472, A053495-A053505, A005388, A261428. Column k=8 of A008307. Sequence in context: A322940 A306519 A001472 * A005388 A053503 A308381 Adjacent sequences:  A053495 A053496 A053497 * A053499 A053500 A053501 KEYWORD nonn AUTHOR N. J. A. Sloane, Jan 15 2000 STATUS approved

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Last modified April 17 08:40 EDT 2021. Contains 343064 sequences. (Running on oeis4.)