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A193131
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Numbers of spanning trees of the complete tripartite graphs K_{n,n,n}.
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2
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3, 384, 419904, 1610612736, 15000000000000, 277326388342554624, 8964455938423371595776, 464227514732017603087171584, 36132988816414656965872925540352, 4026531840000000000000000000000000000
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 3*8^(n-1)*n^(3*n-2).
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MAPLE
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a:= proc(n) local h, i, M;
M:= Matrix(3*n, shape=symmetric);
for h in [seq(seq([[i, j+n], [i, j+2*n], [i+n, j+2*n]][],
j=1..n), i=1..n)]
do M[h[]]:= -1 od;
for i to 3*n do M[i, i]:= -add(M[i, j], j=1..3*n) od;
Determinant(DeleteColumn(DeleteRow(M, 1), 1))
end:
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MATHEMATICA
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Table[3 8^(n - 1) n^(3 n - 2), {n, 11}]
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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