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Search: id:A137782
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| A137782 |
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a(n) = the number of permutations (p(1),p(2),...,p(n)) of (1,2,...,n) where, for each k (2<=k<=n), the sign of (p(k) - p(k-1)) equals the sign of (p(n+2-k) - p(n+1-k)). |
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+0
3
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| 1, 2, 2, 12, 24, 200, 540, 6160, 21616, 306432, 1310880, 22338624, 113017696, 2245983168, 13108918368, 297761967360, 1969736890624, 50332737128960, 372125016868608, 10565549532009472, 86337114225206784
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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First 8 terms calculated by Olivier Gerard.
Number of order n permutations whose descent set is invariant w.r.t. the function f(x)=n-x. [From Max Alekseyev (maxale(AT)gmail.com), May 06 2009]
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LINKS
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Leroy Quet, Home Page (listed in lieu of email address)
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FORMULA
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a(2n) = A000984(n)*A060350(n) [From Max Alekseyev (maxale(AT)gmail.com), Apr 23 2009]
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EXAMPLE
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Consider the permutation (for n = 7):
3,6,7,5,1,2,4
The signs of the differences between adjacent terms forms the sequence: ++--++, which has
reflective symmetry. So this permutation, among others, is counted when n = 7.
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PROGRAM
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(PARI) { a(n) = local(r, u, c, t); r=0; forvec(v=vector(n-1, i, [2*i==n, 1]), u=sum(i=1, #v, v[i]); c=sum(i=1, (n-1)\2, !v[i]&&!v[n-i]); t=[0]; for(i=1, #v, if(v[i], t=concat(t, [i]))); r += (-1)^u * 2^c * n! \ prod(i=2, #t, (t[i]-t[i-1])!) \ (n-t[ #t])! ); (-1)^(n+1)*r } [From Max Alekseyev (maxale(AT)gmail.com), May 06 2009]
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CROSSREFS
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Cf. A137783.
Sequence in context: A092900 A164961 A122007 this_sequence A131384 A052612 A130306
Adjacent sequences: A137779 A137780 A137781 this_sequence A137783 A137784 A137785
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KEYWORD
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nonn
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AUTHOR
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Leroy Quet Feb 10 2008
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EXTENSIONS
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Extended by Max Alekseyev (maxale(AT)gmail.com), Apr 23 2009
Extended by Max Alekseyev (maxale(AT)gmail.com), May 06 2009
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