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A007079 Number of labeled regular tournaments with 2n+1 nodes.
(Formerly M2142)
3
1, 2, 24, 2640, 3230080, 48251508480, 9307700611292160, 24061983498249428379648, 855847205541481495117975879680, 427102683126284520201657800159366676480, 3035991776725501434069099002640396043332019814400, 311112533558482034321687955029997989477274014274150137856000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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

LINKS

Brendan McKay, Table of n, a(n) for n = 0..17

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

B. D. McKay, The asymptotic numbers of regular tournaments, Eulerian digraphs and Eulerian oriented graphs, Combinatorica 10 (1990), 367-377.

Index entries for sequences related to tournaments

FORMULA

a(n) is the 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

(PARI)

a(n)={ local(M=Map());

my(acc(p, v)=my(z); mapput(M, p, if(mapisdefined(M, p, &z), z+v, v)));

my(recurse(p, i, q, v, e)=if(e<=n, if(i<0, acc(x^e+q, v), my(t=polcoeff(p, i)); for(k=0, if(i==n, 0, t), self()(p, i-1, (t-k+x*k)*x^i+q, binomial(t, k)*v, e+t-k)))));

my(iterate(v, k, f)=for(i=1, k, v=f(v)); v);

iterate(Mat([1, 1]), 2*n, src->M=Map(); for(i=1, matsize(src)[1], my(p=src[i, 1]); recurse(p, poldegree(p), 0, src[i, 2], 0)); Mat(M))[1, 2]

} \\ Andrew Howroyd, Jan 08 2018

CROSSREFS

Sequence in context: A184595 A262206 A240993 * A083697 A112332 A110131

Adjacent sequences:  A007076 A007077 A007078 * A007080 A007081 A007082

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane, Mira Bernstein

EXTENSIONS

a(11) from Andrew Howroyd, Jan 08 2018

STATUS

approved

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Last modified January 21 10:25 EST 2022. Contains 350477 sequences. (Running on oeis4.)