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Search: id:A089087
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| A089087 |
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Triangular array of coefficients multiplied by n! of polynomials in e. These give the expected number of trials needed for the sum of uniform random variables from the interval [0,1] to exceeds n+1. |
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1
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| 1, 1, -1, 2, -4, 1, 6, -18, 12, -1, 24, -96, 108, -32, 1, 120, -600, 960, -540, 80, -1, 720, -4320, 9000, -7680, 2430, -192, 1, 5040, -35280, 90720, -105000, 53760, -10206, 448, -1, 40320, -322560, 987840, -1451520, 1050000, -344064, 40824, -1024, 1, 362880, -3265920, 11612160, -20744640, 19595520
(list; table; graph; listen)
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OFFSET
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0,4
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REFERENCES
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J. Derbyshire, "Prime Obsession: Bernhard Riemann and the Greatest Unsolved...", Henry Press, 2003, footnote on page 366.
J. V. Uspenski, "Introduction to Mathematical Probability", McGraw Hill, 1937, p. 278.
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LINKS
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Eric Weisstein's World of Mathematics, More information
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FORMULA
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a(n)=(-1)^k*n!*(n+1-k)^k/k!; n th row, (n = 0, 1, 2, 3...) and k th coefficient (k = 0, 1, 2, 3...)
E.g.f.: 1/(exp(y*x)-x).
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EXAMPLE
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Expected number of uniform random choices of X from interval[0,1] so that their sum exceeds 1 is e/0!. Exceeds 2 is (e^2-e)/1!. Exceeds 3 is (2e^3-4e^2+e)/2!
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CROSSREFS
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Cf. A001113 A090142 A090143 A090137 A090138.
Sequence in context: A110877 A021009 A137478 this_sequence A119303 A105552 A112852
Adjacent sequences: A089084 A089085 A089086 this_sequence A089088 A089089 A089090
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Brian Dunfield (brian.dunfield(AT)sympatico.ca), Dec 04 2003
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)Eunet.yu), Dec 05 2003
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