A296942 Expansion of e.g.f. arcsinh(x*tan(x/2)) (even powers only).
0, 1, 1, -12, -193, 5195, 397248, -9589391, -3147743231, -10931156748, 65632780196255, 4713930109297211, -2846093176389647904, -606335605925899344287, 213167747093485780707937, 109460864600185764327567060, -21782399212761670190907400897
Offset: 0
Keywords
Examples
arcsinh(x*tan(x/2)) = x^2/2! + x^4/4! - 12*x^6/6! - 193*x^8/8! + ...
Crossrefs
Programs
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Mathematica
nmax = 16; Table[(CoefficientList[Series[ArcSinh[x Tan[x/2]], {x, 0, 2 nmax}], x] Range[0, 2 nmax]!)[[n]], {n, 1, 2 nmax + 1, 2}]
Formula
a(n) = (2*n)! * [x^(2*n)] arcsinh(x*tan(x/2)).