A051695 Number of degree-n even permutations of order exactly 4.

0, 0, 0, 0, 0, 90, 630, 3780, 18900, 94500, 457380, 3825360, 31505760, 312432120, 2704501800, 22984481520, 179863997040, 1531709328240, 13078616488560, 147223414987200, 1657733805020160, 20131890668255520, 226464779237447520, 2542924546378413120, 27053572399079688000

Offset: 1

Author

Vladeta Jovovic

Keywords

• easy
• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A001473, A048099, A051685.

Programs

Mathematica

m = 26; ((Exp[x + x^2/2 + x^4/4] + Exp[x - x^2/2 - x^4/4] - Exp[x + x^2/2] - Exp[x - x^2/2])/2 + O[x]^m // CoefficientList[#, x]& // Rest) * Range[m - 1]! (* Jean-François Alcover, Feb 09 2020, after Andrew Howroyd *)

PARI

seq(n)={my(A=O(x*x^n)); Vec(serlaplace(exp(x + x^2/2 + x^4/4 + A) + exp(x - x^2/2 - x^4/4 + A) - exp(x + x^2/2 + A) - exp(x - x^2/2 + A))/2, -n)} \\ Andrew Howroyd, Feb 01 2020

Formula

a(n) = (A001473(n) + A051685(n))/2.

E.g.f.: (exp(x + x^2/2 + x^4/4) + exp(x - x^2/2 - x^4/4) - exp(x + x^2/2) - exp(x - x^2/2))/2. - Andrew Howroyd, Feb 01 2020

Extensions

Terms a(19) and beyond from Andrew Howroyd, Feb 01 2020