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Search: id:A002428
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| A002428 |
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Numerators of coefficients of expansion of arctan(x)^2 = x^2-2/3*x^4+23/45*x^6-44/105*x^8+563/1575*x^10-3254/10395*x^12+ ...
(Formerly M2131 N0844)
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+0
6
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| 0, 1, -2, 23, -44, 563, -3254, 88069, -11384, 1593269, -15518938, 31730711, -186088972, 3788707301, -5776016314, 340028535787, -667903294192, 10823198495797, -5476065119726, 409741429887649, -103505656241356, 17141894231615609
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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|a(n)| = numerator of Sum_{k=1..n} 1/(n(2k-1)).
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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).
A. Fletcher, J. C. P. Miller, L. Rosenhead and L. J. Comrie, An Index of Mathematical Tables. Vols. 1 and 2, 2nd ed., Blackwell, Oxford and Addison-Wesley, Reading, MA, 1962, Vol. 1, p. 89.
H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 313.
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PROGRAM
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(PARI) for(n=1, 30, print1(numerator(sum(k=1, n, 1/(n*(2*k-1)))), ", "))
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CROSSREFS
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Cf. A071968.
Cf. A002549, A004041, A025550, A035048.
Sequence in context: A107374 A068835 A156557 this_sequence A105440 A139831 A049592
Adjacent sequences: A002425 A002426 A002427 this_sequence A002429 A002430 A002431
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KEYWORD
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sign,easy,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 Jason Earls (zevi_35711(AT)yahoo.com), Apr 09 2002
Additional comments from Benoit Cloitre, Apr 06, 2002
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