A061131 Number of degree-n even permutations of order dividing 8.

1, 1, 1, 1, 4, 16, 136, 736, 4096, 20224, 326656, 2970496, 33826816, 291237376, 2129910784, 13607197696, 324498374656, 4599593353216, 52741679343616, 495632154179584, 7127212838772736, 94268828128854016, 2098358019107700736, 34030412427789500416

Offset: 0

Author

Vladeta Jovovic, Apr 14 2001

Keywords

• easy
• nonn

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..502
• Lev Glebsky, Melany Licón, Luis Manuel Rivera, On the number of even roots of permutations, arXiv:1907.00548 [math.CO], 2019.
• T. Koda, M. Sato, Y. Tskegahara, 2-adic properties for the numbers of involutions in the alternating groups, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages).

Crossrefs

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

Programs

PARI

my(x='x+O('x^30)); Vec(serlaplace(1/2*exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) + 1/2*exp(x - 1/2*x^2 - 1/4*x^4 - 1/8*x^8))) \\ Michel Marcus, Jun 18 2019

Formula

E.g.f.: 1/2*exp(x + 1/2*x^2 + 1/4*x^4 + 1/8*x^8) + 1/2*exp(x - 1/2*x^2 - 1/4*x^4 - 1/8*x^8).