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A012758 Expansion of e.g.f. arcsin(cosh(x) * log(x+1)). 0

%I #13 Jul 25 2018 04:09:30

%S 0,1,-1,6,-18,123,-855,8610,-92540,1220765,-17627085,291506270,

%T -5265113502,105134332743,-2272750891411,53258927842666,

%U -1338863892701400,36033888424535961,-1032074699069841561

%N Expansion of e.g.f. arcsin(cosh(x) * log(x+1)).

%F a(n) ~ -(-1)^n * sqrt(1/r + sqrt(1 - r^2)/exp(r)) * n^(n-1) / (exp(n*(1-r)) * (exp(r) - 1)^(n - 1/2)), where r = 0.85490459670313737191040551709068078198... is the real root of the equation 1 + sqrt(1 - r^2) = r*exp(1 - exp(-r)). - _Vaclav Kotesovec_, Jul 25 2018

%e x - 1/2!*x^2 + 6/3!*x^3 - 18/4!*x^4 + 123/5!*x^5 ...

%t Range[0, 20]! CoefficientList[ Series[ArcSin[Cosh[x] Log[x + 1]], {x, 0, 20}], x] (* _Robert G. Wilson v_, Jul 24 2018 *)

%K sign

%O 0,4

%A Patrick Demichel (patrick.demichel(AT)hp.com)

%E a(0) inserted and title improved by _Sean A. Irvine_, Jul 24 2018

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Last modified February 22 21:30 EST 2024. Contains 370265 sequences. (Running on oeis4.)