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A002790
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Denominators of Cauchy numbers of second type (= Bernoulli numbers B_n^{(n)}).
(Formerly M1559 N0608)
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11
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1, 2, 6, 4, 30, 12, 84, 24, 90, 20, 132, 24, 5460, 840, 360, 16, 1530, 180, 7980, 840, 13860, 440, 1656, 720, 81900, 6552, 216, 112, 3480, 240, 114576, 7392, 117810, 2380, 1260, 72, 3838380, 207480, 32760, 560, 568260, 27720, 238392, 55440, 869400, 2576, 236880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| These coefficients (with alternating signs) are also known as the Nørlund [or Norlund or Noerlund] numbers.
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REFERENCES
| L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 294.
L. M. Milne-Thompson, Calculus of Finite Differences, 1951, p. 136.
Guodong Liu, Some computational formulas for Norlund numbers, Fib. Quart., 45 (2007), 133-137.
Merlini, Donatella; Sprugnoli, Renzo; and Verri, M. Cecilia; The Cauchy numbers. Discrete Math. 306 (2006), no. 16, 1906-1920.
N. E. Nørlund, Vorlesungen ueber Differenzenrechnung, Springer-Verlag, Berlin, 1924.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Feng-Zhen Zhao, Sums of products of Cauchy numbers, Discrete Math., 309 (2009), 3830-3842.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
Index entries for sequences related to Bernoulli numbers.
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FORMULA
| Denominator of integral of x(x+1)...(x+n-1) from 0 to 1.
E.g.f.: -x/(1-x)/ln(1-x).
Denominator of Sum_{k=0..n} (-1)^k A008275(n,k)/(k+1). [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
a(n) = A091137(n)/n!. [From Paul Curtz (bpcrtz(AT)free.fr), Nov 27 2008]
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EXAMPLE
| 1, 1/2, 5/6, 9/4, 251/30, 475/12, 19087/84, 36799/24, 1070017/90, ...
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MAPLE
| seq(denom(add((-1)^k*stirling1(n, k)/(k+1), k=0..n)), n=0..20); [From Peter Luschny (peter(AT)luschny.de), Apr 28 2009]
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MATHEMATICA
| Table[ Denominator[ NorlundB[n, n]], {n, 0, 60}] (* From Vladimir Joseph Stephan Orlovsky (4vladimir(AT)gmail.com), 30 Dec 2010 *)
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CROSSREFS
| Cf. A002657. See also A002208, A002209, A002206, A002207, A006232, A006233.
Sequence in context: A057643 A073039 A064538 * A108951 A181822 A174940
Adjacent sequences: A002787 A002788 A002789 * A002791 A002792 A002793
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KEYWORD
| nonn,frac,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Improved readability of the Curtz formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 17 2010
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