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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.)