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A152873
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Number of permutations of {1,2,...,n} (n>=2) having a single run of even entries. For example, the permutation 513284679 has a single run of even entries: 2846.
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1
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2, 6, 12, 48, 144, 720, 2880, 17280, 86400, 604800, 3628800, 29030400, 203212800, 1828915200, 14631321600, 146313216000, 1316818944000, 14485008384000, 144850083840000, 1738201006080000, 19120211066880000, 248562743869440000
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OFFSET
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2,1
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COMMENTS
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a(n) = A152667(n,1).
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LINKS
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Table of n, a(n) for n=2..23.
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FORMULA
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a(2n) = (n+1)(n!)^2;
a(2n+1) = n!(n+2)!
E.g.f.: 24 sqrt(4-x^2)*arcsin(x/2)/[(2-x)^3*(2+x)^2] - x(6-8x-3x^2+2x^3)/ [(2+x)(2-x)^2].
G.f.: G(0)/x^2 -1/x^2 -2/x, where G(k) = 1 + x*(k+2)/(1 - x*(k+1)/ (x*(k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013
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EXAMPLE
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a(4) = 12 because we have 2413, 2431, 4213, 4231, 1243, 1423 and their reverses.
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MAPLE
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ae := proc (n) options operator, arrow: factorial(n)^2*(n+1) end proc: ao := proc (n) options operator, arrow: factorial(n)*factorial(n+2) end proc: a := proc (n) if `mod`(n, 2) = 0 then ae((1/2)*n) else ao((1/2)*n-1/2) end if end proc; seq(a(n), n = 2 .. 23);
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CROSSREFS
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Cf. A152667.
Sequence in context: A169858 A292132 A208147 * A175810 A083001 A285079
Adjacent sequences: A152870 A152871 A152872 * A152874 A152875 A152876
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KEYWORD
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nonn
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AUTHOR
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Emeric Deutsch, Dec 14 2008
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STATUS
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approved
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