A296435 Expansion of e.g.f. log(1 + arcsinh(x)).
0, 1, -1, 1, -2, 13, -64, 173, -720, 12409, -114816, 370137, -1491456, 88556037, -1263184896, 2668274373, 21448022016, 2491377242481, -50233550831616, -34526890553679, 5153298175033344, 202383113207336829, -5453228045913292800, -25792743610973373219, 1393299559788718325760
Offset: 0
Keywords
Examples
E.g.f.: A(x) = x/1! - x^2/2! + x^3/3! - 2*x^4/4! + 13*x^5/5! - 64*x^6/6! + ...
Links
- Robert Israel, Table of n, a(n) for n = 0..451
Programs
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Maple
S:= series(ln(1+arcsinh(x)),x,51): seq(coeff(S,x,j)*j!,j=0..50); # Robert Israel, Dec 12 2017
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Mathematica
nmax = 24; CoefficientList[Series[Log[1 + ArcSinh[x]], {x, 0, nmax}], x] Range[0, nmax]! nmax = 24; CoefficientList[Series[Log[1 + Log[x + Sqrt[1 + x^2]]], {x, 0, nmax}], x] Range[0, nmax]! -
PARI
Vecrev(Pol(serlaplace(log(1 + asinh(x + O(x^30)))))) \\ Andrew Howroyd, Dec 12 2017
Formula
E.g.f.: log(1 + log(x + sqrt(1 + x^2))).
a(n) ~ 4*(Pi*cos(Pi*n/2) + 2*sin(Pi*n/2)) * n^(n-1) / ((4 + Pi^2) * exp(n)). - Vaclav Kotesovec, Dec 21 2017