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 A061131 Number of degree-n even permutations of order dividing 8. 5
 1, 1, 1, 1, 4, 16, 136, 736, 4096, 20224, 326656, 2970496, 33826816, 291237376, 2129910784, 13607197696, 324498374656, 4599593353216, 52741679343616, 495632154179584, 7127212838772736, 94268828128854016, 2098358019107700736, 34030412427789500416 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 8 10:32 EST 2023. Contains 367678 sequences. (Running on oeis4.)