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A002085 From the expansion of sinh x / cos x: a(n) = odd part of A002084(n).
(Formerly M4620 N1973)
2
1, 1, 9, 39, 1141, 12721, 804309, 17113719, 1886573641, 65373260641, 11127809595009, 570506317184199, 138730500808639741, 9867549661639871761 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Eric DuchĂȘne, AS Fraenkel, V Gurvich, Nbao Ho, C. Kimberling, U. Larsson, Wythoff wisdom, Preprint 2016;

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).

LINKS

T. D. Noe, Table of n, a(n) for n=0..50

J. M. Gandhi, The coefficients of sinh x/ cos x. Canad. Math. Bull. 13 1970 305-310.

FORMULA

Divide A002084(n) by 4^(floor((n+1)/4)).

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 *)

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 */

CROSSREFS

Cf. A002084.

Sequence in context: A075210 A146187 A173764 * A076603 A003354 A063164

Adjacent sequences:  A002082 A002083 A002084 * A002086 A002087 A002088

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 20 13:04 EDT 2017. Contains 290835 sequences.