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Search: id:A133333
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| A133333 |
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Olinde Rodrigues recursive polynomial for Inversions of permutations applied to Bonnaci type polynomials: x-1,x^2-x-1, x^3-x^2-x-1, etc.: U(n,x)=Product[x^n-Sun[x^i,{i,0,m-2}],{m,0,n}]. |
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+0
1
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| -1, 1, -1, 3, -3, 1, 1, 4, 2, -8, -5, 8, 2, -4, 1, -1, -5, -15, -25, -25, -1, 25, 35, 5, -15, -21, 5, 5, 5, -5, 1, 1, 6, 21, 56, 114, 186, 246, 246, 171, 34, -114, -174, -149, -54, 54, 66, 51, 6, -34, -6, -6, 4, 9, -6, 1, -1, -7, -28, -84, -210, -448, -833, -1373, -2023, -2653, -3094, -3178, -2793, -1953, -883, 161, 917, 1197
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The polynomial powers grow as : I(n)=n!binomial[n,2]/2
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REFERENCES
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Warren P. Johnson,American Math. Monthly,Oct 2007,volume 114, number 8, pages 752-758
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FORMULA
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U(n,x)=Product[x^n-Sun[x^i,{i,0,m-2}],{m,0,n}] a(n,m)=CoeffiecientList[U[n,x),x]
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EXAMPLE
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{-1},
{1},
{-1, 3, -3, 1},
{1, 4, 2, -8, -5, 8, 2, -4, 1},
{-1, -5, -15, -25, -25, -1, 25, 35, 5, -15, -21, 5, 5, 5, -5, 1},
{1, 6, 21, 56, 114, 186, 246, 246, 171, 34, -114, -174, -149, -54, 54, 66, 51, 6, -34, -6, -6, 4, 9, -6,1},
{-1, -7, -28, -84, -210, -448, -833, -1373, -2023, -2653, -3094, -3178, -2793, -1953, -883, 161, 917, 1197, 987, 567,91, -253, -343, -203, -98, 28, 91, 63, -15, 7, -14, -14, 0, 14, -7, 1},
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MATHEMATICA
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f[q_, n_] = If[n == 0, -1, q^(n - 1) - Sum[q^i, {i, 0, n - 2}]]; g[q_, n_] = Product[f[q, n], {m, 0, n}]; a = Table[CoefficientList[g[x, n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
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Sequence in context: A090569 A160324 A109439 this_sequence A133332 A123562 A046218
Adjacent sequences: A133330 A133331 A133332 this_sequence A133334 A133335 A133336
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KEYWORD
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uned,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 19 2007
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