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 A287231 Number of matchings in the n-triangular graph. 2
 1, 4, 51, 2460, 513619, 509709696, 2590569730617, 71972142178289680, 11572569464349559854105, 11332749125368045400133079296, 70775590368575601248957366910425851, 2939823814188321813975498471683171002746816, 844162736935477006294039214093750952242356035727995, 1736712038520659436678773853448507425382701807453031820800000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS Table of n, a(n) for n=2..15. Eric Weisstein's World of Mathematics, Independent Edge Set Eric Weisstein's World of Mathematics, Johnson Graph Eric Weisstein's World of Mathematics, Matching Eric Weisstein's World of Mathematics, Triangular Graph PROG (PARI) \\ groups all labeled oriented graphs on n vertices by out degree configuration. OrientedByOutDegrees(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, for(k=0, e, acc(x^k+q, binomial(e, k)*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))); (1+sum(i=1, r\2, binomial(r, 2*i)*v[i]))*prod(i=1, h, v[i]^(polcoeff(p, 2*i)+polcoeff(p, 2*i-1)))); my(M=OrientedByOutDegrees(n-1)); sum(i=1, matsize(M)[1], M[i, 2]*c(M[i, 1])) } \\ Andrew Howroyd, Aug 25 2017 CROSSREFS Sequence in context: A220282 A235326 A210834 * A289708 A000516 A182044 Adjacent sequences: A287228 A287229 A287230 * A287232 A287233 A287234 KEYWORD nonn,more AUTHOR Eric W. Weisstein, May 22 2017 EXTENSIONS a(9)-a(12) from Andrew Howroyd, Aug 25 2017 a(13)-a(14) from Eric W. Weisstein, Sep 30 2017 - Oct 01 2017 a(15) from Eric W. Weisstein, Oct 15 2017 STATUS approved

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Last modified June 9 03:24 EDT 2023. Contains 363168 sequences. (Running on oeis4.)