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A326242 Number of degree-n odd permutations of order dividing 12. 2
0, 0, 1, 3, 12, 60, 360, 2016, 11088, 73872, 602640, 4411440, 81677376, 934435008, 8100473472, 104370819840, 1448725616640, 15823660179456, 247231858514688, 3703908371910912, 66727356304757760, 1124506454958351360, 19305439846610835456 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Robert Israel, Table of n, a(n) for n = 0..482

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.: (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) - (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)).

EXAMPLE

For n=3 the a(3)=3 solutions are (1, 2), (2, 3), (1, 3) (permutations in cyclic notation).

MAPLE

E:= (1/2)*exp(x + (1/2)*x^2 + (1/3)*x^3 + (1/4)*x^4 + (1/6)*x^6+(1/12)*x^(12)) - (1/2)*exp(x - (1/2)*x^2 + (1/3)*x^3 - (1/4)*x^4 - (1/6)*x^6-(1/12)*x^(12)):

S:= series(E, x, 31):

seq(coeff(S, x, i)*i!, i=0..30); # Robert Israel, Jul 08 2019

MATHEMATICA

With[{nn = 22}, CoefficientList[Series[1/2 Exp[x + x^2/2 + x^3/3 + x^4/4 + x^6/6 +x^12/12]-1/2 Exp[x - x^2/2 + x^3/3 - x^4/4 - x^6/6 - x^12/12], {x, 0, nn}], x]*Range[0, nn]!]

CROSSREFS

Cf. A053502, A326242, A000704, A061130, A061131, A061132, A048099, A051695, A061133, A061134, A061135, A326241.

Sequence in context: A140097 A105227 A000258 * A070863 A180707 A062569

Adjacent sequences:  A326239 A326240 A326241 * A326243 A326244 A326245

KEYWORD

nonn

AUTHOR

Luis Manuel Rivera Martínez, Jul 06 2019

STATUS

approved

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Last modified August 10 07:14 EDT 2020. Contains 336368 sequences. (Running on oeis4.)