A009837 Expansion of tanh(x)tan(x)/2 in powers of x^(4*n+2).

1, 56, 46336, 182844416, 2205641015296, 63603482126974976, 3748468097940723859456, 404963012992964559934324736, 74035562436962891333631597346816, 21543523644222111882868080329093021696, 9505937948357641883573662624456235995365376

Offset: 0

Author

R. H. Hardin

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..120

Crossrefs

Cf. A024342.

Programs

Magma

m:=50; R:=PowerSeriesRing(Rationals(), m);
b:= Coefficients(R!(Laplace( Tan(x)*Tanh(x)/2 )));
[b[4*n-3]: n in [1..Floor((m-2)/4)]]; // G. C. Greubel, Jan 31 2022

Mathematica

nn=20; Table[(CoefficientList[Series[(Tan[x]*Tanh[x])/2,{x,0,4*nn+2}],x] * Range[0,4*nn+2]!)[[n]],{n,3,4*nn+1,4}] (* Vaclav Kotesovec, Jan 24 2015 *)

Sage

[factorial(4*n+2)*( tan(x)*tanh(x)/2 ).series(x, 4*n+3).list()[4*n+2] for n in (0..20)] # G. C. Greubel, Jan 31 2022

Formula

a(n) = [ x^(4*n+2) ] ( tanh(x)*tan(x)/2 ).

a(n) = A024342(n)/2.

a(n) ~ (4*n+2)! * 2^(4*n+4) * tanh(Pi/2) / Pi^(4*n+3). - Vaclav Kotesovec, Jan 24 2015

Extensions

Extended and signs tested Mar 1997.