A002085 From the expansion of sinh(x) / cos(x): a(n) = odd part of A002084(n).

1, 1, 9, 39, 1141, 12721, 804309, 17113719, 1886573641, 65373260641, 11127809595009, 570506317184199, 138730500808639741, 9867549661639871761, 3247323803322747092109, 305991103023048833011479, 130958280255560469436519441, 15789929076277491342686566081

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• 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
• Eric Duchene, Aviezri S. Fraenkel, Vladimir Gurvich, Nhan Bao Ho, Clark Kimberling, and Urban Larsson, Wythoff Wisdom, 43 pages, no date, unpublished.
• Eric Duchene, Aviezri S. Fraenkel, Vladimir Gurvich, Nhan Bao Ho, Clark Kimberling, and Urban Larsson, Wythoff Wisdom, unpublished, no date. [Cached copy, with permission]
• J. M. Gandhi, The coefficients of sinh x/ cos x. Canad. Math. Bull. 13 1970 305-310.

Crossrefs

Cf. A002084.

Programs

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 *)

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 */

Formula

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

Extensions

Added more terms from b-file. - David Radcliffe, Jul 21 2025