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

0,5

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..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).

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).

Prog

(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

Crossrefs

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

Sequence in context: A363443 A349264 A061129 * A136651 A195899 A362143

Adjacent sequences: A061128 A061129 A061130 * A061132 A061133 A061134

Keyword

easy,nonn

Author

Vladeta Jovovic, Apr 14 2001

Status

approved