OFFSET
1,1
LINKS
Math StackExchange, How do I test for convergence of log(n)/n/sqrt(n+1), (2019)
FORMULA
Equals sum_{l>=0} (-1)^(l+1) (2l-1)!! *Zeta'(3/2+l) /(2l)!!.
EXAMPLE
3.77100949140092...
MAPLE
Digits := 120 ;
x := 0.0 ;
for l from 0 to 600 do
x := x+(-1)^(l+1)*doublefactorial(2*l-1)/doublefactorial(2*l)*Zeta(1, 3/2+l) ;
x := evalf(x) ;
print(x) ;
end do: # R. J. Mathar, Jun 27 2024
PROG
(PARI) default(realprecision, 200); sumalt(k=0, (-1)^(k+1) * (2*k)! * zeta'(k+3/2) / (k!^2 * 4^k)) \\ Vaclav Kotesovec, Jun 27 2024
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
R. J. Mathar, Jun 19 2024
EXTENSIONS
More terms from Vaclav Kotesovec, Jun 27 2024
STATUS
approved