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 A363180 Number of permutations of [2n] with n parity changes. 3
 1, 2, 8, 288, 10368, 1036800, 103680000, 20321280000, 3982970880000, 1290482565120000, 418116351098880000, 202368313931857920000, 97946263943019233280000, 66211674425481001697280000, 44759091911625157147361280000, 40283182720462641432625152000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..225 FORMULA a(n) = A152874(2n,n). From Vaclav Kotesovec, May 26 2023: (Start) Recurrence: (2*n - 3)*a(n) = 4*(2*n^2 - 4*n + 1)*a(n-1) + 16*(n-2)^2*(n-1)^2*(2*n - 1)*a(n-2). a(n) ~ 2^(2*n+1) * n^(2*n) / exp(2*n). (End) EXAMPLE a(0) = 1: (), the empty permutation. a(1) = 2: 12, 21. a(2) = 8: 1243, 1423, 2134, 2314, 3241, 3421, 4132, 4312. a(3) = 288: 123546, 123564, 124356, 124536, 125346, ..., 652431, 653241, 653421, 654213, 654231. MAPLE a:= proc(n) option remember; `if`(n<2, 2^n, (16*(n-2)^2*(2*n-1)*(n-1)^2*a(n-2)+4*(2*n^2-4*n+1)*a(n-1))/(2*n-3)) end: seq(a(n), n=0..18); CROSSREFS Cf. A152874, A363236. Sequence in context: A012301 A296406 A215651 * A285850 A009501 A013027 Adjacent sequences: A363177 A363178 A363179 * A363181 A363182 A363183 KEYWORD nonn AUTHOR Alois P. Heinz, May 23 2023 STATUS approved

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Last modified November 29 06:17 EST 2023. Contains 367422 sequences. (Running on oeis4.)