A003719 Expansion of tan(x)*cosh(x). (Formerly M3996)

1, 5, 41, 685, 19921, 887765, 56126201, 4776869245, 526589630881, 72989204937125, 12424192360405961, 2547879762929443405, 619570064016825283441, 176273806836039238900085, 58010159408189457446855321, 21864887814006548202566779165

Offset

0,2

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=0..15.

Formula

a(n) = Sum_{k>=0} binomial(2n+1, 2k)*A000111(2n+1-2k). - Philippe Deléham, Aug 27 2005

a(n) ~ cosh(Pi/2) * (2*n+1)! * 2^(2*n+3) / Pi^(2*n+2). - Vaclav Kotesovec, Feb 16 2015

Mathematica

nn = 20; Table[(CoefficientList[Series[Cosh[x]*Tan[x], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 16 2015 *)

Crossrefs

Bisection of A009739 and (apparently) A062272.

Sequence in context: A100288 A076094 A076131 * A363884 A181033 A189997

Adjacent sequences: A003716 A003717 A003718 * A003720 A003721 A003722

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and formatted Mar 15 1997 by Olivier Gérard

Prior Mathematica program deleted by Harvey P. Dale, Nov 04 2019

Status

approved