%I A002431 M0124 N0050
%S A002431 1,1,1,2,1,2,1382,4,3617,87734,349222,310732,472728182,2631724,
%T A002431 13571120588,13785346041608,7709321041217,303257395102,52630543106106954746,
%U A002431 616840823966644,522165436992898244102,6080390575672283210764,10121188937927645176372
%V A002431 1,-1,-1,-2,-1,-2,-1382,-4,-3617,-87734,-349222,-310732,-472728182,-2631724,
%W A002431 -13571120588,-13785346041608,-7709321041217,-303257395102,-52630543106106954746,
%X A002431 -616840823966644,-522165436992898244102,-6080390575672283210764,-10121188937927645176372
%N A002431 Numerators in Taylor series for cot x.
%C A002431 Can be written as numerators of multiples of Bernoulli numbers.
%D A002431 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 75 (4.3.70).
%D A002431 G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
%D A002431 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.
%D A002431 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. 74.
%D A002431 H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 
               1, p. 19.
%D A002431 H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer 
               Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 331.
%D A002431 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002431 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002431 T. D. Noe, <a href="b002431.txt">Table of n, a(n) for n=-1..100</a>
%H A002431 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A002431 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/
               Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</
               a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 
               1972, p. 75 (4.3.70).
%H A002431 <a href="Sindx_Be.html#Bernoulli">Index entries for sequences related 
               to Bernoulli numbers.</a>
%H A002431 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Cotangent.html">Cotangent</a>
%F A002431 a(n)=-numerator(A000182[ n ]/(4^n-1)), n>0.
%F A002431 cot x = Sum_{k=0..inf} (-1)^k B_{2k} 4^k x^(2k-1) / (2k)!.
%e A002431 x^(-1)-1/3*x-1/45*x^3-2/945*x^5-1/4725*x^7-2/93555*x^9+O(x^11).
%p A002431 Contribution from Peter Luschny (peter(AT)luschny.de), Jun 08 2009: (Start)
%p A002431 b := n -> (-1)^n*2^(2*n)*bernoulli(2*n)/(2*n)!;
%p A002431 a := n -> numer(b(n+1)); seq(a(i),i=-1..21); (End)
%Y A002431 Cf. A036278 (denominators), A000182.
%Y A002431 Sequence in context: A141238 A094690 A010249 this_sequence A062963 A143255 
               A127139
%Y A002431 Adjacent sequences: A002428 A002429 A002430 this_sequence A002432 A002433 
               A002434
%K A002431 sign,easy,nice
%O A002431 -1,4
%A A002431 N. J. A. Sloane (njas(AT)research.att.com).