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Search: id:A055134
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| A055134 |
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Triangle read by rows: T(n,k) = number of labeled endofunctions on n points with k fixed points. |
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+0
3
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| 1, 0, 1, 1, 2, 1, 8, 12, 6, 1, 81, 108, 54, 12, 1, 1024, 1280, 640, 160, 20, 1, 15625, 18750, 9375, 2500, 375, 30, 1, 279936, 326592, 163296, 45360, 7560, 756, 42, 1, 5764801, 6588344, 3294172, 941192, 168070, 19208, 1372, 56, 1, 134217728
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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The same triangle (except for signs) may be obtained from the determinants of the Brahmagupta matrices, setting x->Sqrt[z], y->1, t->n. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
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REFERENCES
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Weisstein, Eric W. "Brahmagupta Matrix." http://mathworld.wolfram.com/BrahmaguptaMatrix.html
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FORMULA
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T(n, k) = C(n, k)*(n-1)^(n-k).
E.g.f.: (-LambertW(-y)/y)^(x-1)/(1+LambertW(-y)) (from Vladeta Jovovic (vladeta(AT)Eunet.yu))
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EXAMPLE
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1; 0,1; 1,2,1; 8,12,6,1; 81,108,54,12,1; ...
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MATHEMATICA
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Clear[B] B[0] = {{x, y}, {t*y, x}}; B[n_] := B[n] = B[n - 1].B[0]; Table[Det[B[n]] /. x -> Sqrt[z] /. y -> 1 /. t -> n, {n, 0, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[B[n]] /. x -> Sqrt[z] /. y ->1 /. t -> n, z], {n, 0, 10}]]; Flatten[a] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 09 2008
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CROSSREFS
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Cf. A055135, A055136. Column 0 given in A007778.
Sequence in context: A011019 A007026 A118708 this_sequence A137370 A102735 A088960
Adjacent sequences: A055131 A055132 A055133 this_sequence A055135 A055136 A055137
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Apr 25 2000
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