-1,4

Can be written as numerators of multiples of Bernoulli numbers.

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).

G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 88.

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.

H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1, p. 19.

H. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 331.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n=-1..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

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).

Index entries for sequences related to Bernoulli numbers.

Eric Weisstein's World of Mathematics, Cotangent

a(n)=-numerator(A000182[ n ]/(4^n-1)), n>0.

cot x = Sum_{k=0..inf} (-1)^k B_{2k} 4^k x^(2k-1) / (2k)!.

x^(-1)-1/3*x-1/45*x^3-2/945*x^5-1/4725*x^7-2/93555*x^9+O(x^11).

Contribution from Peter Luschny (peter(AT)luschny.de), Jun 08 2009: (Start)

b := n -> (-1)^n*2^(2*n)*bernoulli(2*n)/(2*n)!;

a := n -> numer(b(n+1)); seq(a(i), i=-1..21); (End)

Cf. A036278 (denominators), A000182.

Sequence in context: A141238 A094690 A010249 this_sequence A062963 A143255 A127139

Adjacent sequences: A002428 A002429 A002430 this_sequence A002432 A002433 A002434

sign,easy,nice

N. J. A. Sloane (njas(AT)research.att.com).