|
%I #7 May 12 2021 06:19:42
%S 0,1,5,26,126,408,-1704,-51696,-555408,-1217664,93550464,2424183552,
%T 30038190336,-114098181120,-16707096806400,-459530721441792,
%U -5231858686838784,130925278326915072,9038174050387722240,246578101419998380032,1534994756662100557824
%N Expansion of e.g.f. log(1 + (1/(1-x)^5 - 1)/5).
%C In general, column k > 2 of A308497 is asymptotic to -2*(n-1)! * cos(n*arctan(sin(Pi/k)/(cos(Pi/k) - (k-1)^(1/k)))) / (1 + 1/(k-1)^(2/k) - 2*cos(Pi/k)/(k-1)^(1/k))^(n/2).
%F a(n) ~ -2*(n-1)! * cos(n*arctan(5^(1/4) / (phi^(1/2)*(phi - 2^(7/5))))) / (1 + 1/2^(4/5) - phi/2^(2/5))^(n/2), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio.
%t nmax = 25; CoefficientList[Series[Log[1 + (1/(1 - x)^5 - 1)/5], {x, 0, nmax}], x] * Range[0, nmax]!
%Y Column k=5 of A308497.
%K sign
%O 0,3
%A _Vaclav Kotesovec_, May 12 2021
|
