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A036278
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Denominators in Taylor series for cot x.
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4
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1, 3, 45, 945, 4725, 93555, 638512875, 18243225, 162820783125, 38979295480125, 1531329465290625, 13447856940643125, 201919571963756521875, 11094481976030578125, 564653660170076273671875, 5660878804669082674070015625, 31245110285511170603633203125
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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REFERENCES
| 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.
H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1, p. 19.
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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, 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).
Eric Weisstein's World of Mathematics, Cotangent
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FORMULA
| cot x = Sum_{k=0..inf} (-1)^k B_{2k} 4^k x^(2k-1) / (2k)!.
a(n)=denominator(A000182[ n ]/(4^n-1)), n>0.
a(n) same denominator for coth x;
coth(x)=W(0)/x -1, W(k)=k+1+2*x-2*x*(k+1)/W(k+1); (continued fraction). - Sergei N. Gladkovskii, Nov 27 2011
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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).
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MATHEMATICA
| Denominator[Select[List@@Series[Cot[x], {x, 0, 40}][[3]], #!=0&]] (* From Harvey P. Dale, Apr 11 2011 *)
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CROSSREFS
| Cf. A002431 (numerators).
Sequence in context: A202437 A008931 A171079 * A154289 A171080 A188681
Adjacent sequences: A036275 A036276 A036277 * A036279 A036280 A036281
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KEYWORD
| nonn,frac,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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