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Coefficients arising from the Taylor series expansion of log(arcsin(x)/log(1+x)).
2

%I #29 Aug 16 2018 03:24:29

%S 0,0,0,0,7,-13,219,-598,11570,-44280,995254,-4960662,126624718,

%T -783821598,22344623929,-166137700653,5222279193717,-45502938763929,

%U 1561364880901471,-15643758252397591,581233980566953138,-6596831160162093686,263618530870787131186,-3348367300606844944161

%N Coefficients arising from the Taylor series expansion of log(arcsin(x)/log(1+x)).

%C a(n) is the truncation of (n! times the coefficient of x^n in the expansion of log(arcsin(x)/log(x+1))). ("Truncate" - this is Maple's definition - means "truncate a number to the next nearest integer towards 0".)

%C Computed by _Sean A. Irvine_, Aug 08 2018, in an attempt to explain the erroneous entry A013568.

%H Robert Israel, <a href="/A317209/b317209.txt">Table of n, a(n) for n = 1..450</a>

%p S:= series(log(arcsin(x)/log(1+x)),x,31):

%p seq(trunc(coeff(S,x,n)*n!),n=1..30); # _Robert Israel_, Aug 10 2018

%Y Cf. A013568.

%K sign

%O 1,5

%A _N. J. A. Sloane_, Aug 10 2018, based on a suggestion from _Sean A. Irvine_, Aug 08 2018

%E More terms and corrected comment from _Robert Israel_, Aug 10 2018