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A073410
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Number of permutations p of (1,2,3,...,n) such that 1*(-1)^p(1)+2*(-1)^p(2)+3*(-1)^p(3)+...+n*(-1)^p(n)=0.
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0
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0, 0, 2, 8, 0, 0, 576, 4608, 0, 0, 2505600, 30067200, 0, 0, 53444966400, 855119462400, 0, 0, 3587014803456000, 71740296069120000, 0, 0
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OFFSET
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1,3
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COMMENTS
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Equivalently the number of grand Dyck n-paths in which each run length is selected from {1..2*n} without replacement. - David Scambler, Apr 16 2013
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LINKS
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Table of n, a(n) for n=1..22.
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FORMULA
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It seems that a(n)=0 if n==1 or 2 (mod 4) and a(4*k)=4*k*a(4*k-1). - Benoit Cloitre, Aug 23 2002
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PROG
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(PARI) a(n)=sum(k=1, n!, if(sum(i=1, n, i*(-1)^component(numtoperm(n, k), i)), 0, 1))
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CROSSREFS
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Sequence in context: A077548 A050809 A095217 * A021361 A199156 A073001
Adjacent sequences: A073407 A073408 A073409 * A073411 A073412 A073413
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KEYWORD
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nonn,more
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AUTHOR
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Benoit Cloitre, Aug 23 2002
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EXTENSIONS
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More terms from John W. Layman, Feb 05 2003
a(14)-a(22) from Robert Gerbicz, Nov 22 2010
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STATUS
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approved
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