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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. 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-François 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 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.)