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A002085
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Expansion of sinh x / cos x.
(Formerly M4620 N1973)
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1
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1, 1, 9, 39, 1141, 12721, 804309, 17113719, 1886573641, 65373260641, 11127809595009, 570506317184199, 138730500808639741, 9867549661639871761
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| J. M. Gandhi, The coefficients of sinh x/ cos x. Canad. Math. Bull. 13 1970 305-310.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
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FORMULA
| Divide A002084(n) by 4^(floor((n+1)/4)).
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MATHEMATICA
| a[ n_] := If[ n < 0, 0, SeriesCoefficient[ Sinh[x] / Cos[x], {x, 0, 2 n + 1}] (2 n + 1)! / 2^(n + Mod[n, 2])] (* Michael Somos, Apr 10 2011 *)
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PROG
| (PARI) {a(n) = local(A, m); if( n<0, 0, m = 2*n + 1; A = x * O(x^m) ; 2^(n + 1 - n%2) * m! * polcoeff( sinh( x/2 + A) / cos( x/2 + A), m))} /* Michael Somos, Apr 10 2011 */
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CROSSREFS
| Cf. A002084.
Sequence in context: A075210 A146187 A173764 * A076603 A003354 A063164
Adjacent sequences: A002082 A002083 A002084 * A002086 A002087 A002088
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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