|
%I #13 Mar 27 2019 10:03:57
%S 0,1,1,3,0,28,-85,1029,-6440,79136,-724305,9982005,-118974856,
%T 1858582100,-27126378357,478338929509,-8227405849840,162502213354272,
%U -3209170996757057,70409595412300877,-1566861832498793248,37885426233247176772,-936732798302547171509,24780850678372964078189
%N Expansion of e.g.f. log(1 + arcsin(x))*exp(x).
%H Andrew Howroyd, <a href="/A296436/b296436.txt">Table of n, a(n) for n = 0..200</a>
%F E.g.f.: log(1 - i*log(i*x + sqrt(1 - x^2)))*exp(x), where i is the imaginary unit.
%F a(n) ~ -(-1)^n * sqrt(Pi) * 2^((n + 1)/2) * n^(n - 1/2) / (exp(n + sin(1)) * (1 - cos(2))^(n/2)). - _Vaclav Kotesovec_, Dec 21 2017
%e E.g.f.: A(x) = x/1! + x^2/2! + 3*x^3/3! + 28*x^5/5! - 85*x^6/6! + 1029*x^7/7! - 6440*x^8/8! + ...
%p a:=series(log(1+arcsin(x))*exp(x),x=0,24): seq(n!*coeff(a,x,n),n=0..23); # _Paolo P. Lava_, Mar 27 2019
%t nmax = 23; CoefficientList[Series[Log[1 + ArcSin[x]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
%t nmax = 23; CoefficientList[Series[Log[1 - I Log[I x + Sqrt[1 - x^2]]] Exp[x], {x, 0, nmax}], x] Range[0, nmax]!
%o (PARI) my(ox=O(x^30)); Vecrev(Pol(serlaplace(log(1 + asin(x + ox)) * exp(x + ox)))) \\ _Andrew Howroyd_, Dec 12 2017
%Y Cf. A009334, A009337, A009353, A189815, A291482, A296437.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Dec 12 2017
|
