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A261683
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Number of permutations p of {1..2n} such that p[2k-1]<p[2k] <=> p[2k]<p[2k+1].
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6
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2, 8, 84, 1632, 51040, 2340480, 147985824, 12338740736, 1311694023168, 173163464017920, 27793189979315200, 5329882370469617664, 1203569385876087300096, 316106247473967737765888, 95541594110304706706657280, 32926404311225961897742172160
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OFFSET
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1,1
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COMMENTS
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The relation between p[2n-1] and p[2n] is arbitrary; hence a(n) = 2*n*A122647(n). a(n) is also (surprisingly) the number of 2 X n whirlpool permutations (see link, also A334518). - Don Knuth, May 06 2020.
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LINKS
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FORMULA
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Basset (2014, Eq. (4)) gives a g.f.
a(n) = (2n)! [z^(2n)] 2*sqrt(2)*z*(exp(sqrt(2)*z)-1) / (2+sqrt(2)*z + (2-sqrt(2)*z)*exp(sqrt(2)*z)). - Alois P. Heinz, Sep 06 2015
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MAPLE
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egf:= 2*(x->1/(1-x*tanh(x))-1)(z/sqrt(2)):
a:= n-> (2*n)!*coeff(series(egf, z, 2*n+1), z, 2*n):
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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