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Search: id:A119502
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| 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 24, 6, 2, 1, 1, 120, 24, 6, 2, 1, 1, 720, 120, 24, 6, 2, 1, 1, 5040, 720, 120, 24, 6, 2, 1, 1, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 3628800, 362880, 40320, 5040, 720, 120, 24, 6, 2, 1, 1, 39916800
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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The reciprocal of each entry in a lower triangular readout of the exponential of a matrix whose entry {j+1,j} equals one (and all other entries are zero). Note all said entries are unit fractions (all numerators are one).
Denominators of unfinished fractional coefficients for polynomials 152650/A152656 =A009998/A119052. [From Paul Curtz (bpcrtz(AT)free.fr), Dec 13 2008]
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FORMULA
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T(n,k) = (n-k)! a(n) = Gamma[binomial[1 + Floor[(1/2) + Sqrt[2*(1 + n)]], 2] - n]
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EXAMPLE
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1; 1, 1; 2, 1, 1; 6, 2, 1, 1; 24, 6, 2, 1, 1; ...
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MATHEMATICA
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Table[Gamma[Binomial[1 + Floor[(1/2) + Sqrt[2*(1 + n)]], 2] - n], {n, 0, 77}]
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CROSSREFS
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Cf. A025581.
Sequence in context: A125731 A123361 A107106 this_sequence A142156 A136707 A085826
Adjacent sequences: A119499 A119500 A119501 this_sequence A119503 A119504 A119505
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), May 26 2006
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