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A033815
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Number of standard permutations of [ a_1..a_n b_1..b_n ] (b_i is not immediately followed by a_i, for all i).
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4
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1, 1, 14, 426, 24024, 2170680, 287250480, 52370755920, 12585067447680, 3854801333416320, 1465957162768492800, 677696237345719468800, 374281829360322587827200, 243388909697235614324812800, 184070135024053703140543027200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also turns up as the solution to Problem #18, p. 326 of Alan Tucker's Applied Combinatorics, 4th ed, Wiley NY 2002 [Tucker's `n' is the `2n' here]. - John L Leonard, Sep 15 2003
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REFERENCES
| Leo Chao, Paul DesJarlais and John L Leonard, A binomial identity, via derangements, Math. Gaz. 89 (2005), 268-270..
R. P. Stanley, Enumerative Combinatorics I, Chap.2, Exercise 10, p. 89.
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LINKS
| Ira Gessel, Enumerative applications of symmetric functions
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FORMULA
| a(n)=2n(2n-1)a(n-1)+n(n-1)a(n-2); a(n)=sum(binomial(n, i)*(-1)^i*(2*n-i)!, i=0..n).
a(n) = sum_{i=0}^n [ {nchoose i} (2n-i)! sum_{j=0}^{2n-i} (-1)^j/j! ]; also a(n) = n! sum_{i=0}^n {nchoose i} n!/(n-i)! [ sum_{j=0}^{n-i} (-1)^j {n-i choose j} (n-j)!/i! ]. - John L Leonard, Sep 15 2003
a(n) = Sum_{k=0..n} binomial(n,k)*A000166(n+k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 04 2006
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MAPLE
| A033815 := proc(n) local i; add(binomial(n, i)*(-1)^i*(2*n - i)!, i = 0 .. n) end;
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CROSSREFS
| A002119[ n ]*n!.
Main diagonal of array in A068106.
Sequence in context: A097310 A041367 A041364 * A187358 A103916 A201546
Adjacent sequences: A033812 A033813 A033814 * A033816 A033817 A033818
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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