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A133332
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Olinde Rodrigues recursive polynomial for Inversions of permutations: U(n,x)=Product[Sun[x^i,{i,0,m-1}],{m,0,n}].
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0
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1, 1, 1, 3, 3, 1, 1, 4, 10, 16, 19, 16, 10, 4, 1, 1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1, 1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506, 1246, 951, 666, 426, 246, 126, 56, 21, 6, 1, 1, 7, 28, 84, 210, 462, 917
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OFFSET
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1,4
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COMMENTS
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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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LINKS
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Table of n, a(n) for n=1..63.
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FORMULA
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U(n,x)=Product[Sun[x^i,{i,0,m-1}],{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, 10, 16, 19, 16, 10, 4, 1},
{1, 5, 15, 35, 65, 101, 135, 155, 155, 135, 101, 65, 35, 15, 5, 1},
{1, 6, 21, 56, 126, 246, 426, 666, 951, 1246, 1506, 1686, 1751, 1686, 1506,1246, 951, 666, 426, 246, 126, 56, 21, 6, 1},
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MATHEMATICA
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f[q_, n_] = If[n == 0, 1, Sum[q^i, {i, 0, n - 1}]]; g[q_, n_] = Product[f[q, n], {m, 0, n}]; a = Table[CoefficientList[g[x, n], x], {n, 0, 10}]
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CROSSREFS
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Sequence in context: A109439 A133333 A171876 * A179680 A123562 A046218
Adjacent sequences: A133329 A133330 A133331 * A133333 A133334 A133335
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula, Oct 19 2007
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STATUS
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approved
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