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

1,6

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A001473, A048099, A051685.

Sequence in context: A367093 A065949 A224541 * A304165 A232588 A097372

Adjacent sequences: A051692 A051693 A051694 * A051696 A051697 A051698

Keyword

easy,nonn

Author

Vladeta Jovovic

Extensions

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

Status

approved