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Search: id:A137783
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| A137783 |
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a(n) = the number of permutations (p(1),p(2),...,p(2n+1)) of (1,2,...,2n+1) where, for each k (2<=k<=2n+1), the sign of (p(k) - p(k-1)) equals the sign of (p(2n+2-k) - p(2n+3-k)). |
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+0
2
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| 1, 4, 44, 1028, 40864, 2484032, 214050784, 24831582176, 3731039384576, 704879630525696, 163539441616948736, 45712130697710081024, 15150993151215400441856, 5875388829103413298173952, 2635427286694074346846232576, 1353918066433734600362650169344
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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There are no such permutations of (1,2,...,2n).
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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EXAMPLE
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Consider the permutation (for n = 3): 3,4,5,2,7,6,1. The signs of the differences between adjacent terms forms the sequence: ++-+--, which is the negative of its reversal. So this permutation, among others, is counted when n = 3.
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PROGRAM
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(PARI) { a(n) = local(s, c, r); s=0; forvec(t=vector(n\2, i, [0, 2]), c=0; r=[]; for(j=1, #t, if(t[j]==0, c++, if(t[j]==1, r=concat(r, [j]), r=concat(r, [n-j])); ); ); r=vecsort(r); s+=(-2)^c*if(#r, n!/(r[1]!*prod(j=1, #r-1, (r[j+1]-r[j])!)*(n-r[ #r])!), 1) ); s }
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CROSSREFS
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Cf. A137782.
Sequence in context: A144827 A144004 A053333 this_sequence A136552 A155556 A127635
Adjacent sequences: A137780 A137781 A137782 this_sequence A137784 A137785 A137786
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Feb 10 2008, Feb 14 2008
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EXTENSIONS
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First 4 terms calculated by Olivier Gerard.
Edited and extended by Max Alekseyev (maxale(AT)gmail.com), May 09 2009
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