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 A130705 Floors of constants in De Bruijn's approach to weighted Carleman's inequality. 0
 -109, -42, -26, -18, -14, -12, -10, -9, -8, -7, -6, -6, -5, -5, -5, -4, -4, -4, -4, -4, -3, -3, -3, -3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -2, -1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS From Gao's abstract: "We study finite sections of weighted Carleman's inequality following the approach of De Bruijn. Similar to the unweighted case, we obtain an asymptotic expression for the optimal constant." REFERENCES N. G. De Bruijn, Carleman's inequality for finite series, Nederl. Akad. Wetensch. Proc. Ser. A 66 = Indag, pp. 505-514. LINKS Peng Gao, Finite Sections of Weighted Carleman's Inequality, arXiv:0707.0077 FORMULA a(n) = floor(e - (2*(pi^2)*e)/((log(n))^2)). EXAMPLE a(2) = -109 because e - (2*(pi^2)*e)/((log(2))^2) ~ -108.9611770171388392925257212314455433803548032218666994709. a(3) = -42 because e - (2*(pi^2)*e)/((log(3))^2) ~ -41.7382232411477828847325690963577817095329948893743754723. a(4) = -26 because e - (2*(pi^2)*e)/((log(4))^2) ~ -25.20158288294042589661121470434688897177076548519170518650. a(30) = -2 because e - (2*(pi^2)*e)/((log(30))^2) ~ -1.92003649778404604739381818236913112747520. a(45) = -1 because e - (2*(pi^2)*e)/((log(45))^2) ~ -0.98456269963010489451493724472555817336322761419762175593. CROSSREFS Sequence in context: A077728 A093724 A247440 * A253431 A253438 A263194 Adjacent sequences:  A130702 A130703 A130704 * A130706 A130707 A130708 KEYWORD easy,sign AUTHOR Jonathan Vos Post, Jul 03 2007 EXTENSIONS Replaced arxiv URL by non-cached version - R. J. Mathar, Oct 30 2009 STATUS approved

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)