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Search: id:A002209
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| A002209 |
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Denominators of coefficients for numerical integration.
(Formerly M2015 N0796)
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+0
9
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| 1, 2, 12, 8, 720, 288, 60480, 17280, 3628800, 89600, 95800320, 17418240, 2615348736000, 402361344000, 4483454976000, 98402304, 32011868528640000, 342372925440000, 51090942171709440000, 5377993912811520000, 33720021833328230400000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) is the denominator of the "reverse" multiple zeta value zeta_n^R(0,0,...,0) for n>0. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Nov 29 2006
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Akiyama and Y. Tanigawa, Multiple zeta values at non-positive integers, Ramanujan J. 5 (2001), 327-351.
Charles Jordan, Calculus of Finite Differences, Chelsea 1965, p. 529.
A. N. Lowan and H. Salzer, Table of coefficients in numerical integration formulae, J. Math. Phys., 22 (1943), 49-50.
Guodong Liu, Some computational formulas for Norlund numbers, Fib. Quart., 45 (2007), 133-137.
N. E. Noerlund, Vorlesungen ueber Differenzenrechnung, Springer-Verlag, Berlin, 1924.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..100
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FORMULA
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G.f.: -x/((1-x)*ln(1-x)).
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EXAMPLE
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1, 1/2, 5/12, 3/8, 251/720, 95/288, 19087/60480, 5257/17280, 1070017/3628800, 25713/89600, 26842253/95800320, 4777223/17418240, 703604254357/2615348736000, 106364763817/402361344000, ... = A002208/A002209
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CROSSREFS
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Cf. A002208. See also A002657, A002790, A002206, A002207, A006232, A006233.
Sequence in context: A133437 A014964 A001898 this_sequence A100654 A166544 A081468
Adjacent sequences: A002206 A002207 A002208 this_sequence A002210 A002211 A002212
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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