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A036280
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Numerators in Taylor series for cosec x.
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5
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1, 1, 7, 31, 127, 73, 1414477, 8191, 16931177, 5749691557, 91546277357, 3324754717, 1982765468311237, 22076500342261, 65053034220152267, 925118910976041358111, 16555640865486520478399, 8089941578146657681, 29167285342563717499865628061
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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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 (4.3.68).
G. W. Caunt, Infinitesimal Calculus, Oxford Univ. Press, 1914, p. 477.
J. Malenfant, Factorization of and Determinant Expressions for the Hypersums of Powers of Integers, Arxiv preprint arXiv:1104.4332, 2011.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..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 (4.3.68).
Eric Weisstein's World of Mathematics, Hyperbolic Cosecant
Eric Weisstein's World of Mathematics, Cosecant
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FORMULA
| Numerator of sum_{k=1..2*n-2} sum_{j=1..k} 2^(1-j) *(-1)^(n+j-1) *binomial(k,j) *sum_{i=0..floor(j/2)} (j-2*i)^(2*n+j-2) *binomial(j,i) *(-1)^i /(2*n+j-2)!, n>1. [From Vladimir Kruchinin, Apr 12 2011]
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EXAMPLE
| x^(-1)+1/6*x+7/360*x^3+31/15120*x^5+...
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MAPLE
| series(csc(x), x, 60);
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PROG
| (Maxima)
a(n):=num(sum(sum((2^(1-j)*(-1)^(n+j-1)*binomial(k, j)*sum((j-2*i)^(2*n+j-2)*binomial(j, i)*(-1)^(i), i, 0, floor(j/2)))/(2*n+j-2)!, j, 1, k), k, 1, 2*n-2)); n>1. a(1)=1. /* From Vladimir Kruchinin, Apr 12 2011 */
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CROSSREFS
| Cf. A036281, also A036282, A036283.
Sequence in context: A125193 A002184 A002588 * A153005 A056909 A002147
Adjacent sequences: A036277 A036278 A036279 * A036281 A036282 A036283
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KEYWORD
| nonn,frac,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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