Search: id:A001896
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%I A001896 M4403 N1858
%S A001896 1,1,7,31,127,2555,1414477,57337,118518239,5749691557,91546277357,
%T A001896 1792042792463,1982765468311237,286994504449393,3187598676787461083,
%U A001896 4625594554880206790555,16555640865486520478399,22142170099387402072897
%V A001896 1,-1,7,-31,127,-2555,1414477,-57337,118518239,-5749691557,91546277357,
%W A001896 -1792042792463,1982765468311237,-286994504449393,3187598676787461083,
%X A001896 -4625594554880206790555,16555640865486520478399,-22142170099387402072897
%N A001896 Numerators of cosecant numbers -2*(2^(2*n-1)-1)*Bernoulli(2*n); also 
               of Bernoulli(2n,1/2) and Bernoulli(2n,1/4).
%C A001896 Cosecant number are given by the integral: (-Pi^2)^(-n)*int((ln(x/(1-x)))^2*n,
               x=0..1) [From Groux roland (roland.groux(AT)orange.fr), Nov 10 2009]
%D A001896 H. T. Davis, Tables of the Mathematical Functions. Vols. 1 and 2, 2nd 
               ed., 1963, Vol. 3 (with V. J. Fisher), 1962; Principia Press of Trinity 
               Univ., San Antonio, TX, Vol. 2, p. 187.
%D A001896 S. A. Joffe, Sums of like powers of natural numbers, Quart. J. Pure Appl. 
               Math. 46 (1914), 33-51.
%D A001896 D. H. Lehmer, Lacunary recurrence formulas for the numbers of Bernoulli 
               and Euler, Annals Math., 36 (1935), 637-649.
%D A001896 N. E. N\"{o}rlund, Vorlesungen \"{u}ber Differenzenrechnung. Springer-Verlag, 
               Berlin, 1924, p. 458.
%D A001896 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001896 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001896 Hector Blandin and Rafael Diaz, <a href="http://arXiv.org/pdf/0708.0809">
               Compositional Bernoulli numbers</a>, Page 7, 3rd table, (B^sin)_1,
               n is identical to |A001896| / A001897.
%H A001896 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%F A001896 with(numtheory); [ seq(bernoulli(2*n, 1/2), n=0..20) ];
%e A001896 1, -1/12, 7/240, -31/1344, 127/3840, -2555/33792, 1414477/5591040, -57337/
               49152, 118518239/16711680, ... = A001896/A033469
%e A001896 Cosecant numbers -2*(2^(2*n-1)-1)*Bernoulli(2*n) are 1, -1/3, 7/15, -31/
               21, 127/15, -2555/33, 1414477/1365, -57337/3, 118518239/255, -5749691557/
               399, 91546277357/165, -1792042792463/69, 1982765468311237/1365, -286994504449393/
               3, 3187598676787461083/435, ... = A001896/A001897.
%Y A001896 Cf. A001897, A033469.
%Y A001896 Cf. A132092-A132106.
%Y A001896 Sequence in context: A083420 A036282 A033474 this_sequence A044049 A005825 
               A086901
%Y A001896 Adjacent sequences: A001893 A001894 A001895 this_sequence A001897 A001898 
               A001899
%K A001896 sign
%O A001896 0,3
%A A001896 N. J. A. Sloane (njas(AT)research.att.com).

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