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A324361
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Total number of occurrences of n in the (signed) displacement sets of all permutations of [2n] divided by n!.
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3
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0, 1, 5, 49, 679, 12151, 266321, 6906257, 206788751, 7020426511, 266464077769, 11180868467209, 513915970996583, 25678820830238759, 1385874945753239969, 80341660921985676961, 4979071555472111291551, 328496221117149603559327, 22987138271050177264124441
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..366
Wikipedia, Permutation
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FORMULA
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a(n) = n! [x^n] (1-exp(-x))/(1-x)^(n+1).
a(n) = -1/n! * Sum_{j=1..n} (-1)^j * binomial(n,j) * (2n-j)!.
a(n) = (8*n-12)*a(n-1) - (16*n^2-64*n+59)*a(n-2) - (4*n-10)*a(n-3) for n > 2.
a(n) = A324362(n,n) = A306234(2n,n).
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MAPLE
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a:= proc(s) option remember; `if`(n<3, (3*n-1)*n/2,
(8*n-12)*a(n-1)-(16*n^2-64*n+59)*a(n-2)-(4*n-10)*a(n-3))
end:
seq(a(n), n=0..20);
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CROSSREFS
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Main diagonal of A324362.
Cf. A000142, A306234.
Sequence in context: A297513 A228511 A116873 * A089914 A267220 A052142
Adjacent sequences: A324358 A324359 A324360 * A324362 A324363 A324364
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Feb 23 2019
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STATUS
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approved
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