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A113248
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Number of permutations pi in S_n such that maj pi and maj pi^(-1) have opposite parity where maj is the major index. Equivalently, the number of pi such that maj pi and inv pi have opposite parity where inv is the inversion number.
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2
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0, 0, 2, 8, 56, 336, 2496, 19968, 181248, 1812480, 19956480, 239477760, 3113487360, 43588823040, 653836861440, 10461389783040, 177843708887040, 3201186759966720, 60822550111518720, 1216451002230374400
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OFFSET
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0,3
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COMMENTS
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a(2n) and a(2n+1) are both divisible by 2^n n! a(2n) = 2n a(2n-1) The number of pi in S_n such that maj pi is even and maj pi^(-1) is odd is exactly half of a(n)
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LINKS
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FORMULA
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a(2n) = 2 n^2 a(2n-2) + 2 n (n-1) b(2n-2) and a(2n+1) = 2 n (n+1) a(2n-1) + 2 n^2 b(2n-1) where b(n) is sequence A113247
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EXAMPLE
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a(3)=2 because the following 2 permutations in S_3 have opposite parity for their major index and the major index of their inverse: 231, 312.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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