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A061137
Number of degree-n odd permutations of order dividing 6.
3
0, 0, 1, 3, 6, 30, 270, 1386, 6048, 46656, 387180, 2469060, 17204616, 158065128, 1903506696, 18887563800, 163657221120, 2095170230016, 30792968596368, 346564643468976, 3905503235814240, 58609511127871200, 866032039742528736
OFFSET
0,4
LINKS
Lev Glebsky, Melany Licón, Luis Manuel Rivera, On the number of even roots of permutations, arXiv:1907.00548 [math.CO], 2019.
FORMULA
E.g.f.: exp(x + x^3/3)*sinh(x^2/2 + x^6/6).
Linear recurrence of order 12 whose coefficients are polynomials in n of degree up to 15: see link. - Robert Israel, Jul 13 2018
MAPLE
Egf:= exp(x + x^3/3)*sinh(x^2/2 + x^6/6):
S:= series(Egf, x, 31):
seq(coeff(S, x, j)*j!, j=0..30); # Robert Israel, Jul 13 2018
MATHEMATICA
With[{m=30}, CoefficientList[Series[Exp[x + x^3/3]*Sinh[x^2/2 + x^6/6], {x, 0, m}], x]*Range[0, m]!] (* Vincenzo Librandi, Jul 02 2019 *)
PROG
(PARI) my(x='x+O('x^30)); concat([0, 0], Vec(serlaplace( exp(x + x^3/3)*sinh(x^2/2 + x^6/6) ))) \\ G. C. Greubel, Jul 02 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x + x^3/3)*Sinh(x^2/2 + x^6/6) )); [0, 0] cat [Factorial(n+1)*b[n]: n in [1..m-2]]; // G. C. Greubel, Jul 02 2019
(Sage) m = 30; T = taylor(exp(x + x^3/3)*sinh(x^2/2 + x^6/6), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Jul 02 2019
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Apr 14 2001
STATUS
approved