A061129 Number of degree-n even permutations of order dividing 4.

1, 1, 1, 1, 4, 16, 136, 736, 4096, 20224, 99856, 475696, 3889216, 31778176, 313696384, 2709911296, 23006784256, 179965340416, 1532217039616, 13081112406784, 147235213351936, 1657791879049216, 20132199908571136, 226466449808367616, 2542933338768769024

Offset

0,5

Links

Alois P. Heinz, Table of n, a(n) for n = 0..570

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)*cosh(x^2/2 + x^4/4).

Mathematica

With[{n=30}, CoefficientList[Series[Exp[x]*Cosh[x^2/2 + x^4/4], {x, 0, n}], x]*Range[0, n]!] (* G. C. Greubel, Jul 02 2019 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace( exp(x)*cosh(x^2/2 + x^4/4) )) \\ G. C. Greubel, Jul 02 2019
(Magma) m:=30; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp(x)*Cosh(x^2/2 + x^4/4) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Jul 02 2019
(Sage) m = 30; T = taylor(exp(x)*cosh(x^2/2 + x^4/4), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Jul 02 2019

Crossrefs

Cf. A000085, A001470, A001472, A052501, A053496 - A053505, A001189, A001471, A001473, A061121 - A061128, A000704, A061129 - A061132, A048099, A051695, A061133 - A061135.

Sequence in context: A323552 A363443 A349264 * A061131 A136651 A195899

Adjacent sequences: A061126 A061127 A061128 * A061130 A061131 A061132

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 14 2001

Status

approved