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 A297565 Number of maximum matchings in the n-triangular graph. 1
 1, 3, 8, 144, 47520, 16656192, 3321907200, 21173194506240, 7866775374741504000, 1714731229742768455680000, 149617202324844553489612800000, 1023015704130692419403265343488000000, 822671651496871196689402715812984258560000000, 267398413297417500827783894166564037306456473600000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Eric W. Weisstein, Table of n, a(n) for n = 2..18 Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Maximum Independent Edge Set Eric Weisstein's World of Mathematics, Triangular Graph PROG (PARI) \\ groups all orientations of n-complete graph by out degree configuration. CompleteOrientationsByOutDegrees(n)={ \\ high memory usage and slow for n > 10 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(i<0, acc(x^e+q, v), my(t=polcoeff(p, i)); for(k=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]), n-1, 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)) } a(n)={ my(v=vector(n\2, n, (2*n)!/(2^n*n!))); my(c(p)=my(h=(poldegree(p)+1)\2); my(r=n-1-sum(i=1, h, polcoeff(p, 2*i-1))); if(r%2, n*r/2, 1)*if(r<2, 1, v[r\2])*prod(i=1, h, v[i]^(polcoeff(p, 2*i)+polcoeff(p, 2*i-1)))); my(M=CompleteOrientationsByOutDegrees(n-1)); sum(i=1, matsize(M)[1], M[i, 2]*c(M[i, 1])) } \\ Andrew Howroyd, Jan 02 2018 CROSSREFS Cf. A287231, A297484. Sequence in context: A132491 A083112 A053605 * A289884 A076147 A132563 Adjacent sequences:  A297562 A297563 A297564 * A297566 A297567 A297568 KEYWORD nonn AUTHOR Eric W. Weisstein, Dec 31 2017 EXTENSIONS a(10)-a(15) and offset corrected by Andrew Howroyd, Jan 02 2018 a(16)-a(18) from Eric W. Weisstein, Jan 06-08 2018 STATUS approved

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Last modified August 12 00:34 EDT 2022. Contains 356067 sequences. (Running on oeis4.)