A296980
Expansion of e.g.f. arcsinh(log(1 + x)).
Original entry on oeis.org
0, 1, -1, 1, 0, -2, -30, 446, -3248, 12412, 16020, -211356, -10756944, 284038272, -3556910448, 19122463296, 135073768320, -1286054192304, -108801241372368, 3952903127312016, -65667347037774720, 339816855220730784, 8862271481944986336
Offset: 0
arcsinh(log(1 + x)) = x^1/1! - x^2/2! + x^3/3! - 2*x^5/5! - 30*x^6/6! + ...
Cf.
A001710,
A001818,
A003703,
A003708,
A009024,
A009454,
A009775,
A104150,
A296435,
A296979,
A296981,
A296982.
-
a:=series(arcsinh(log(1+x)),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 26 2019
-
nmax = 22; CoefficientList[Series[ArcSinh[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Log[Log[1 + x] + Sqrt[1 + Log[1 + x]^2]], {x, 0, nmax}], x] Range[0, nmax]!
A296981
Expansion of e.g.f. arctan(log(1 + x)).
Original entry on oeis.org
0, 1, -1, 0, 6, -22, -30, 952, -5656, -9952, 508320, -3874992, -20690208, 833780400, -7697940432, -52230156288, 2467649024640, -24686997151104, -329724479772288, 14493628861307136, -159114034671287040, -2682505451050592256, 126421889770129637376
Offset: 0
arctan(log(1 + x)) = x^1/1! - x^2/2! + 6*x^4/4! - 22*x^5/5! - 30*x^6/6! + ...
Cf.
A001710,
A003703,
A003708,
A009024,
A009454,
A009775,
A010050,
A104150,
A110708,
A296979,
A296980,
A296982.
-
a:=series(arctan(log(1+x)),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 26 2019
-
nmax = 22; CoefficientList[Series[ArcTan[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[(I/2) Log[1 - I Log[1 + x]] - (I/2) Log[1 + I Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
A296982
Expansion of e.g.f. arctanh(log(1 + x)).
Original entry on oeis.org
0, 1, -1, 4, -18, 118, -930, 8888, -98504, 1248784, -17790480, 281590032, -4901447232, 93064850448, -1914144990576, 42396742460928, -1006101059149440, 25466710774651776, -684902462140798848, 19503187752732408576, -586221766070655432960
Offset: 0
arctanh(log(1 + x)) = x^1/1! - x^2/2! + 4*x^3/3! - 18*x^4/4! + 118*x^5/5! - 930*x^6/6! + ...
Cf.
A001710,
A003703,
A003708,
A009024,
A009454,
A009775,
A010050,
A104150,
A202139,
A296979,
A296980,
A296981.
-
a:=series(arctanh(log(1+x)),x=0,21): seq(n!*coeff(a,x,n),n=0..20); # Paolo P. Lava, Mar 26 2019
-
nmax = 20; CoefficientList[Series[ArcTanh[Log[1 + x]], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Log[1 + Log[1 + x]]/2 - Log[1 - Log[1 + x]]/2, {x, 0, nmax}], x] Range[0, nmax]!
Showing 1-3 of 3 results.