

A012939


tan(tan(x)+sin(x))=2*x+17/3!*x^3+609/5!*x^5+47183/7!*x^7...


1



2, 17, 609, 47183, 6302193, 1287739735, 373294251737, 145684622344879, 73644231787309153, 46808510431782973735, 36537199084739607908105, 34359533746606613833938495, 38314231054861075994802320721
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OFFSET

0,1


LINKS



FORMULA

a(n) ~ 2 * (cos(r))^2 * (2*n+1)!/ ((1+(cos(r))^3) * r^(2*n+2)), where r = 0.73353218673425082268537645786831692941686010886986150015... is the root of the equation tan(r) + sin(r) = Pi/2. Also r = arcsin(t), where t = 0.66949756462634544159490365... is the root of the equation 4*t^4  4*Pi*t^3 + Pi^2*t^2 + 4*Pi*t  Pi^2 = 0.  Vaclav Kotesovec, Feb 07 2015


MATHEMATICA

nn = 20; Table[(CoefficientList[Series[Tan[Sin[x] + Tan[x]], {x, 0, 2*nn+1}], x] * Range[0, 2*nn+1]!)[[n]], {n, 2, 2*nn, 2}] (* Vaclav Kotesovec, Feb 07 2015 *)


CROSSREFS



KEYWORD

nonn


AUTHOR

Patrick Demichel (patrick.demichel(AT)hp.com)


STATUS

approved



