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A373862

Decimal expansion of Sum_{k >= 1} log(k)/(k*sqrt(k+1)).

3, 7, 7, 1, 0, 0, 9, 4, 9, 1, 4, 0, 0, 9, 2, 3, 2, 2, 6, 0, 7, 9, 0, 8, 1, 1, 3, 7, 6, 7, 7, 3, 3, 8, 4, 1, 2, 4, 3, 5, 0, 9, 3, 6, 9, 9, 8, 4, 2, 2, 3, 1, 9, 0, 7, 3, 0, 0, 0, 9, 4, 4, 5, 9, 5, 9, 1, 8, 9, 2, 3, 5, 5, 0, 5, 6, 2, 1, 7, 4, 2, 9, 2, 2, 9, 0, 5, 2, 2, 9, 5, 7, 1, 7, 9, 9, 3, 6, 0, 5, 6, 7, 4, 6, 3 (list; constant; graph; refs; listen; history; text; internal format)

	OFFSET	`1,1`
	LINKS	`Table of n, a(n) for n=1..105.` `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(2l-1)/doublefactorial(2l)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) * (2k)! zeta'(k+3/2) / (k!^2 * 4^k)) \\ Vaclav Kotesovec, Jun 27 2024`
	CROSSREFS	`Cf. A131688.` `Sequence in context: A009467 A258982 A227336 * A353049 A288093 A131608` `Adjacent sequences: A373859 A373860 A373861 * A373863 A373864 A373865`
	KEYWORD	`nonn,cons`
	AUTHOR	`R. J. Mathar, Jun 19 2024`
	EXTENSIONS	`More terms from Vaclav Kotesovec, Jun 27 2024`
	STATUS	`approved`

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Last modified September 12 12:03 EDT 2024. Contains 375851 sequences. (Running on oeis4.)