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%I #21 Dec 29 2014 19:34:05
%S 3,384,419904,1610612736,15000000000000,277326388342554624,
%T 8964455938423371595776,464227514732017603087171584,
%U 36132988816414656965872925540352,4026531840000000000000000000000000000
%N Numbers of spanning trees of the complete tripartite graphs K_{n,n,n}.
%H Alois P. Heinz, <a href="/A193131/b193131.txt">Table of n, a(n) for n = 1..50</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CompleteTripartiteGraph.html">Complete Tripartite Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SpanningTree.html">Spanning Tree</a>
%F a(n) = 3*8^(n-1)*n^(3*n-2).
%p a:= proc(n) local h, i, M;
%p M:= Matrix(3*n, shape=symmetric);
%p for h in [seq(seq([[i, j+n],[i, j+2*n],[i+n, j+2*n]][],
%p j=1..n), i=1..n)]
%p do M[h[]]:= -1 od;
%p for i to 3*n do M[i, i]:= -add(M[i, j], j=1..3*n) od;
%p Determinant(DeleteColumn(DeleteRow(M, 1), 1))
%p end:
%p seq(a(n), n=1..12); # _Alois P. Heinz_, Jul 18 2011
%t Table[3 8^(n - 1) n^(3 n - 2), {n, 11}]
%o (PARI) a(n)=3*n^(3*n-2)<<(3*n-3) \\ _Charles R Greathouse IV_, Jul 29 2011
%K nonn,easy
%O 1,1
%A _Eric W. Weisstein_, Jul 16 2011
%E More terms from _Alois P. Heinz_, Jul 18 2011
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