|
Search: id:A033815
|
|
|
| A033815 |
|
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). |
|
+0
4
|
|
| 1, 1, 14, 426, 24024, 2170680, 287250480, 52370755920, 12585067447680, 3854801333416320, 1465957162768492800, 677696237345719468800, 374281829360322587827200, 243388909697235614324812800, 184070135024053703140543027200
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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
|
|
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.
|
|
LINKS
|
Ira Gessel, Enumerative applications of symmetric functions
|
|
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
|
|
MAPLE
|
A033815 := proc(n) local i; add(binomial(n, i)*(-1)^i*(2*n - i)!, i = 0 .. n) end;
|
|
CROSSREFS
|
A002119[ n ]*n!.
Main diagonal of array in A068106.
Sequence in context: A097310 A041367 A041364 this_sequence A103916 A005790 A128051
Adjacent sequences: A033812 A033813 A033814 this_sequence A033816 A033817 A033818
|
|
KEYWORD
|
nonn,easy,nice
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
