1,3

a(n) appears to be a multiple of A046990(n) (checked up to n=250). - R. Stephan, Mar 30 2004

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

The Taylor series for tan(x) appears to be identical to the quotient of the 'look-a-likes' of the numerator and denominator, i.e. A160469(n)/A156769(n).

(End)

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).

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 75 (4.3.67).

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. A. Rothe, in C. F. Hindenburg, editor, Sammlung Combinatorisch-Analytischer Abhandlungen, Vol. 2, Chap. XI. Fleischer, Leipzig, 1800, p. 329.

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 (4.3.67).

Eric Weisstein's World of Mathematics, Hyperbolic Tangent

Eric Weisstein's World of Mathematics, Tangent

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

a(n) = numer((-1)^(n-1)*2^(2*n)*(2^(2*n)-1)* bernoulli(2*n)/(2*n)!)

(End)

tan(x) = x + 2 x^3/3! + 16 x^5/5! + 272 x^7/7! + ... = x + 1/3*x^3 + 2/15*x^5 + 17/315*x^7 + 62/2835*x^9 + O(x^10).

tanh(x) = x - 1/3*x^3 + 2/15*x^5 - 17/315*x^7 + 62/2835*x^9 - 1382/155925*x^11 + ...

Cf. A036279 (denominators), A000182.

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), May 24 2009: (Start)

Cf. A160469 and A156769

(End)

Sequence in context: A100518 A125200 A071402 this_sequence A160469 A037420 A034721

Adjacent sequences: A002427 A002428 A002429 this_sequence A002431 A002432 A002433

nonn,easy,frac

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

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Jan 29 2003