A296438
Expansion of e.g.f. log(1 + arctan(x))*exp(x).
Original entry on oeis.org
0, 1, 1, 0, 0, 13, 5, -336, -56, 18593, -6735, -1598520, 1192664, 205475645, -255011835, -36324220856, 62049925040, 8519764352097, -18835422533375, -2551646722754512, 6927586371061712, 951619735931190157, -3077560879933239899, -432185107142832520576, 1624964470900980885432
Offset: 0
E.g.f.: A(x) = x/1! + x^2/2! + 13*x^5/5! + 5*x^6/6! - 336*x^7/7! - 56*x^8/8! + ...
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a:=series(log(1+arctan(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019
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nmax = 24; CoefficientList[Series[Log[1 + ArcTan[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 24; CoefficientList[Series[Log[1 + I (Log[1 - I x] - Log[1 + I x])/2] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
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my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + atan(x + ox)) * exp(x + ox)))) \\ Andrew Howroyd, Dec 12 2017
A297213
Expansion of e.g.f. log(1 + arctanh(x))*exp(-x).
Original entry on oeis.org
0, 1, -3, 10, -40, 213, -1383, 11002, -100616, 1062625, -12508067, 164543938, -2368224032, 37311284645, -634900302775, 11658800863330, -229004281334768, 4804124787023265, -106986109080667043, 2524701174424967130, -62860054802079553016, 1648303843512405478485
Offset: 0
log(1 + arctanh(x))*exp(-x) = x/1! - 3*x^2/2! + 10*x^3/3! - 40*x^4/4! + 213*x^5/5! - 1383*x^6/6! + ...
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S:= series(log(1+arctanh(x))*exp(-x),x,51):
seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Jul 09 2018
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nmax = 21; CoefficientList[Series[Log[1 + ArcTanh[x]] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 21; CoefficientList[Series[Log[1 + (Log[1 + x] - Log[1 - x])/2] Exp[-x], {x, 0, nmax}], x] Range[0, nmax]!
A295278
Expansion of e.g.f. log(1 + x*sech(x))*exp(x).
Original entry on oeis.org
0, 1, 1, -1, 0, 4, -5, 13, -392, 2112, 7663, -165067, 1011560, -2965756, -11164309, 630876517, -12760548400, 133046910432, -189966787521, -18567623055795, 392188656574896, -5061972266268844, 33655544331988203, 565132153437469165, -26647451471277927416
Offset: 0
log(1 + x*sech(x))*exp(x) = x/1! + x^2/2! - x^3/3! + 4*x^5/5! - 5*x^6/6! + ...
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a:=series(log(1+x*sech(x))*exp(x),x=0,25): seq(n!*coeff(a,x,n),n=0..24); # Paolo P. Lava, Mar 27 2019
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nmax = 24; CoefficientList[Series[Log[1 + x Sech[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
A297206
Expansion of e.g.f. log(1 + x*cosh(x))*exp(x).
Original entry on oeis.org
0, 1, 1, 5, 0, 44, -245, 1917, -17976, 191760, -2268017, 29862645, -432485152, 6819543964, -116400819509, 2138673633397, -42078450265744, 882702459984256, -19667723002057473, 463866294631620941, -11545312970532620104, 302416006623761207804, -8316019118849688156693
Offset: 0
log(1 + x*cosh(x))*exp(x) = x/1! + x^2/2! + 5*x^3/3! + 44*x^5/5! - 245*x^6/6! + ...
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a:=series(log(1 + x*cosh(x))*exp(x),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 26 2019
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nmax = 22; CoefficientList[Series[Log[1 + x Cosh[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
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x='x+O('x^99); concat([0], Vec(serlaplace(exp(x)*log(1+x*cosh(x))))) \\ Altug Alkan, Dec 28 2017
Showing 1-4 of 4 results.