A009611 Expansion of sinh(tan(x)*x).

0, 2, 8, 216, 8896, 553120, 48069504, 5564225408, 827281160192, 153537251480064, 34761966006691840, 9422306473314752512, 3010196845995598430208, 1118714469509146379657216, 478278367951534466053799936, 232972682112352062801913282560

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..238

Vaclav Kotesovec, Graph - asymptotic ratio

Formula

a(n) ~ n^(2*n-1/4) * 2^(4*n-3/4) * exp(2*sqrt(2*n)-2*n-1/2) / Pi^(2*n) * (1 - (Pi^2-1)/(12*sqrt(2*n))). - Vaclav Kotesovec, Jan 24 2015

Mathematica

With[{nn=40}, Take[CoefficientList[Series[Sinh[Tan[x]*x], {x, 0, nn}], x] Range[ 0, nn]!, {1, -1, 2}]] (* Harvey P. Dale, Jun 23 2014 *)

Crossrefs

Sequence in context: A012297 A000893 A030177 * A015176 A013345 A013343

Adjacent sequences: A009608 A009609 A009610 * A009612 A009613 A009614

Keyword

nonn

Author

R. H. Hardin

Extensions

Extended and signs tested Mar 15 1997 by Olivier Gérard.

Prior Mathematica program replaced by and more terms from Harvey P. Dale, Jun 23 2014

Status

approved