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Search: id:A002683
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| A002683 |
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Numerators of coefficients for repeated integration.
(Formerly M4421 N1868)
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+0
2
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| 1, -7, 37, -199, 40321, -5512813, 136601407, -32373535937, 4039314145093, -377880467185583, 123905113265594071, -53834048464836263969, 66351862106782030159, -194322297839115779164331, 149128127842572749235559291, -25454412383565669030714950177
(list; graph; listen)
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OFFSET
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0,2
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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).
H. E. Salzer, Coefficients for repeated integration with central differences, Journal of Mathematics and Physics, 28 (1949), 54-61.
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FORMULA
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a(n) is the numerator of -(n/2)M(n)-(2n+2)M(n+1), where M(n)=(2/(2n+1)!)*int(t*product(t^2-k^2, k=1..n), t=0..1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
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MAPLE
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M:=n->(2/(2*n+1)!)*int(t*product(t^2-k^2, k=1..n), t=0..1): B:=n->-(n/2)*M(n)-(2*n+2)*M(n+1): seq(numer(B(n)), n=0..16); (Deutsch)
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CROSSREFS
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Cf. A002195, A002196, A002684.
Sequence in context: A117130 A002807 A124610 this_sequence A126475 A077239 A046235
Adjacent sequences: A002680 A002681 A002682 this_sequence A002684 A002685 A002686
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KEYWORD
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sign,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 25 2005
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