A002085 From the expansion of sinh(x) / cos(x): a(n) = odd part of A002084(n). (Formerly M4620 N1973)

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

Offset

0,3

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S. Fraenkel, Vladimir Gurvich, Nhan Bao Ho, Clark Kimberling, and Urban Larsson, Wythoff Wisdom, 43 pages, no date, unpublished.

Eric Duchene, Aviezri S. Fraenkel, Vladimir Gurvich, Nhan Bao Ho, Clark Kimberling, and Urban Larsson, Wythoff Wisdom, unpublished, no date.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.

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: A146187 A173764 A331343 * A076603 A346336 A003354

Adjacent sequences: A002082 A002083 A002084 * A002086 A002087 A002088

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved