A096716
Denominators of terms in series expansion of tan(sin(x)).
Original entry on oeis.org
1, 6, 40, 5040, 24192, 39916800, 6227020800, 37362124800, 355687428096000, 24329020081766400, 51090942171709440000, 2872446304320552960000, 5170403347776995328000000, 2177773890083670432153600000, 8841761993739701954543616000000, 249176928914482509628047360000000
Offset: 0
tan(sin(x)) = x + 1/6*x^3 - 1/40*x^5 - 107/5040*x^7 - 73/24192*x^9 + 41897/39916800*x^11 + ...
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Denominator[Take[CoefficientList[Series[Tan[Sin[x]], {x,0,50}], x], {2, -1, 2}]] (* G. C. Greubel, Nov 21 2016 *)
A096712
Numerators of terms in series expansion of tan(sin(x)).
Original entry on oeis.org
1, 1, -1, -107, -73, 41897, 3027637, 986527, -11832720271, -238031459363, 22592230600813, 2567503517437949, 877962977779386211, -72551800185828715163, -189312598480126813670107, -555004914636991112974483, 10604546643258382904627047649, 1588669342302765693238039021451
Offset: 0
x+1/6*x^3-1/40*x^5-107/5040*x^7-73/24192*x^9+41897/39916800*x^11+...
A296677
Expansion of e.g.f. arctan(arcsin(x)) (odd powers only).
Original entry on oeis.org
1, -1, 13, -173, 12409, -370137, 88556037, -2668274373, 2491377242481, 34526890553679, 202383113207336829, 25792743610973373219, 39172126704113226631401, 12501799823936578879327095, 15717805122762984314778029685, 9078237580992214462785729689355
Offset: 0
arctan(arcsin(x)) = x/1! - x^3/3! + 13*x^5/5! - 173*x^7/7! + 12409*x^9/9! - 370137*x^11/11! + ...
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nmax = 16; Table[(CoefficientList[Series[ArcTan[ArcSin[x]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
nmax = 16; Table[(CoefficientList[Series[(I/2) Log[1 - Log[I x + Sqrt[1 - x^2]]] - (I/2) Log[1 + Log[I x + Sqrt[1 - x^2]]], {x, 0, 2 nmax + 1}], x] Range[0, 2 nmax + 1]!)[[n]], {n, 2, 2 nmax, 2}]
A352606
Expansion of e.g.f. tan(cos(x) - 1) (even part).
Original entry on oeis.org
0, -1, 1, -31, 421, -19531, 873841, -67417351, 6079224061, -745862759491, 109749390119881, -20006355219508351, 4313763491717212501, -1101230418170874812731, 326019382476444960095521, -111246859639685180908387831, 43247270290320815515213664941
Offset: 0
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my(N=40, x='x+O('x^N)); v=Vec(serlaplace(tan(cos(x)-1))); concat(0, vector(#v\2, k, v[2*k-1]))
Showing 1-4 of 4 results.