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

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

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

References

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

Crossrefs

Bisection of A009739 and (apparently) A062272.

Programs

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 *)

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

Extensions

Extended and formatted Mar 15 1997 by Olivier Gérard

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