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 A048099 Number of degree-n even permutations of order exactly 2. 18
 0, 0, 0, 3, 15, 45, 105, 315, 1323, 5355, 18315, 63855, 272415, 1264263, 5409495, 22302735, 101343375, 507711375, 2495918223, 11798364735, 58074029055, 309240315615, 1670570920095, 8792390355903, 46886941456575, 264381946998975, 1533013006902975, 8785301059346175, 50439885753378303 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..200 Koda, Tatsuhiko; Sato, Masaki; Takegahara, Yugen; 2-adic properties for the numbers of involutions in the alternating groups, J. Algebra Appl. 14 (2015), no. 4, 1550052 (21 pages). FORMULA a(n) = (A001189(n) + A051684(n))/2. a(n) = Sum_{i=1..floor(n/4)} binomial(n,4i)(4i)!/(2^(2i)(2i)!). - Luis Manuel Rivera Martínez, May 16 2018 E.g.f.: (exp(x + x^2/2) + exp(x - x^2/2))/2 - exp(x). - Andrew Howroyd, Feb 01 2020 MATHEMATICA Table[Sum[Binomial[n , 4 i] (4 i)!/(2^(2 i) (2 i)!), {i, 1, Floor[n/4]}], {n, 1, 22}] (* Luis Manuel Rivera Martínez, May 16 2018 *) PROG (PARI) a(n) = sum(i=1, n\4, binomial(n, 4*i)*(4*i)!/(2^(2*i)*(2*i)!)); \\ Michel Marcus, May 17 2018 (PARI) seq(n)={my(A=O(x*x^n)); Vec(serlaplace(exp(x + x^2/2 + A) + exp(x - x^2/2 + A) - 2*exp(x + A))/2, -n)} \\ Andrew Howroyd, Feb 01 2020 CROSSREFS Cf. A001189, A051695. A column of A057740. Sequence in context: A334078 A094191 A050534 * A030505 A301632 A074355 Adjacent sequences:  A048096 A048097 A048098 * A048100 A048101 A048102 KEYWORD easy,nonn AUTHOR STATUS approved

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Last modified August 10 07:57 EDT 2022. Contains 356036 sequences. (Running on oeis4.)