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A007079 Number of labeled regular tournaments with 2n+1 nodes.
(Formerly M2142)
1
1, 2, 24, 2640, 3230080, 48251508480, 9307700611292160, 24061983498249428379648, 855847205541481495117975879680 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

B. D. McKay, Applications of a technique for labeled enumeration, Congress. Numerantium, 40 (1983), 207-221.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..8.

Index entries for sequences related to tournaments

FORMULA

a(n) = coefficient of (x1 x2 ... xn)^((n-1)/2) in (x1+x2)(x1+x3)...(x(n-1)+xn) - Jim Ferry (ferry(AT)metsci.com), Sep 29 2005

MATHEMATICA

(* This program is not convenient for more than 5 terms *)

a[n_] := (xx = Sequence @@ Table[ {x[k], 0, n}, {k, 1, 2*n + 1}]; Coefficient[ Normal @ Series[ Product[x[j] + x[k], {j, 1, (2*n + 1) - 1}, {k, j + 1, (2*n + 1)}], xx], Product[x[j] , {j, 1, (2*n + 1)}]^(((2*n + 1) - 1)/2)]); a[0] = 1; Table[a[n], {n, 0, 4}] (* Jean-Fran├žois Alcover, Apr 10 2013 *)

PROG

(PARI) /* not convenient for more than 5 terms: */

sym(k)=eval(Str("x" k));

pr(n)=prod(j=1, n-1, prod(k=j+1, n, sym(j) + sym(k) ) );

a(n)=

{

    my( p = pr(2*n+1) );

    for (k=1, 2*n+1, p = polcoeff(p, n, sym(k) );  );

    return( p );

}

/* Joerg Arndt, Apr 10 2013 */

CROSSREFS

Sequence in context: A163086 A053995 A184595 * A083697 A110131 A112332

Adjacent sequences:  A007076 A007077 A007078 * A007080 A007081 A007082

KEYWORD

nonn,nice,more

AUTHOR

N. J. A. Sloane, Mira Bernstein

STATUS

approved

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Last modified April 25 03:36 EDT 2014. Contains 240994 sequences.