A061132 Number of degree-n even permutations of order dividing 10.

1, 1, 1, 1, 4, 40, 190, 610, 1660, 13420, 174700, 1326700, 30818800, 342140800, 2534931400, 16519411000, 143752426000, 4842417082000, 73620307162000, 687934401562000, 17165461784680000, 308493094924720000, 4585953613991980000, 53843602355379220000

Offset

0,5

References

J. Riordan, An Introduction to Combinatorial Analysis, John Wiley & Sons, Inc. New York, 1958 (Chap 4, Problem 22).

Links

Alois P. Heinz, Table of n, a(n) for n = 0..491

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 + 1/5*x^5 + 1/10*x^10) + 1/2*exp(x - 1/2*x^2 + 1/5*x^5 - 1/10*x^10).

Example

For n=4 the a(4)=4 solutions are (1), (1, 2)(3, 4), (1, 3)(2, 4), (1, 4)(2, 3) (permutations in cyclic notation). - Luis Manuel Rivera Martínez, Jun 18 2019

Mathematica

With[{nn = 22}, CoefficientList[Series[1/2 Exp[x + x^2/2 + x^5/5 + x^10/10] + 1/2 Exp[x - x^2/2 + x^5/5 - x^10/10], {x, 0, nn}], x]* Range[0, nn]!] (* Luis Manuel Rivera Martínez, Jun 18 2019 *)

Prog

(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/2*exp(x + 1/2*x^2 + 1/5*x^5 + 1/10*x^10) + 1/2*exp(x - 1/2*x^2 + 1/5*x^5 - 1/10*x^10))) \\ Michel Marcus, Jun 18 2019

Crossrefs

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

Sequence in context: A238328 A009355 A355838 * A215717 A270099 A271274

Adjacent sequences: A061129 A061130 A061131 * A061133 A061134 A061135

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 14 2001

Status

approved