A296941 Expansion of e.g.f. arcsin(x*tan(x/2)) (even powers only).
0, 1, 1, 18, 227, 12125, 542448, 55071205, 5492843269, 905996551626, 159770279801855, 39299019878991521, 10721872262093222016, 3707660329253983397113, 1438816154956071399594457, 668949924061617421125859650, 348908555505788456739965412203
Offset: 0
Keywords
Examples
arcsin(x*tan(x/2)) = x^2/2! + x^4/4! + 18*x^6/6! + 227*x^8/8! + ...
Crossrefs
Programs
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Mathematica
nmax = 16; Table[(CoefficientList[Series[ArcSin[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)] arcsin(x*tan(x/2)).