Logo

Greetings from The On-Line Encyclopedia of Integer Sequences!

Hints

Search: id:A002431
Displaying 1-1 of 1 results found. page 1
     Format: long | short | internal | text      Sort: relevance | references | number      Highlight: on | off
A002431 Numerators in Taylor series for cot x.
(Formerly M0124 N0050)
+0
3
1, -1, -1, -2, -1, -2, -1382, -4, -3617, -87734, -349222, -310732, -472728182, -2631724, -13571120588, -13785346041608, -7709321041217, -303257395102, -52630543106106954746, -616840823966644, -522165436992898244102, -6080390575672283210764, -10121188937927645176372 (list; graph; listen)
OFFSET

-1,4

COMMENT

Can be written as numerators of multiples of Bernoulli numbers.

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, December 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.

LINKS

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, December 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, December 1972, p. 75 (4.3.70).

Index entries for sequences related to Bernoulli numbers.

Eric Weisstein's World of Mathematics, Cotangent

FORMULA

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)!.

EXAMPLE

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

CROSSREFS

Cf. A036278 (denominators), A000182.

Sequence in context: A141238 A094690 A010249 this_sequence A062963 A127139 A071431

Adjacent sequences: A002428 A002429 A002430 this_sequence A002432 A002433 A002434

KEYWORD

sign,easy,nice

AUTHOR

njas

page 1

Search completed in 0.002 seconds

Lookup | Welcome | Find friends | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
More pages | Superseeker | Maintained by N. J. A. Sloane (njas@research.att.com)

Last modified July 25 07:41 EDT 2008. Contains 142293 sequences.


AT&T Labs Research