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

Author

Vladeta Jovovic, Apr 14 2001

Keywords

• easy
• nonn

Examples

			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
		

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.

Crossrefs

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

Programs

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 *)

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

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).