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 A242596 Numerators for partial sums of dilog(1/2). 1
 1, 9, 83, 1337, 33497, 5587, 136919, 35054939, 946522553, 946538429, 114531943709, 458129108861, 77423915447309, 38711978428267, 9677996861569, 19820539601545337, 5728136204565261593, 1909378773465525731, 689285743475945831291, 344642873149232707087 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The denominators are given as 2*A242597. The limit of r(n) = a(n)/(2*A242597(n)) for n -> infinity is dilog(1/2) = Li_2(1/2) = sum(1/(k^2*2^k),k=1..infinity) = (Pi^2 - 6*(log(2))^2)/12 = 0.582240526465... For the decimal expansion see A076788. See the Abramowitz-Stegun link, p. 1004, 27.7.3 for x=1/2, and the Jolley reference pp. 66-69, (360) (c). See also Jolley, pp. 22-23 (116). This entry was motivated by eight times the sum over the reciprocals of A243456(2*k) for k >= 5. See a comment given there. REFERENCES L. B. W. Jolley, Summation of Series, Dover (1961). LINKS M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. FORMULA a(n) = numerator(r(n)), with the rational r(n) := sum(1/(k^2*2^k), k=1..n) in lowest terms. EXAMPLE The rationals r(n) are, for n=1, ..., 16: 1/2, 9/16, 83/144, 1337/2304, 33497/57600, 5587/9600, 136919/235200, 35054939/60211200, 946522553/1625702400, 946538429/1625702400, 114531943709/196709990400, 458129108861/786839961600, 77423915447309/132975953510400, 38711978428267/66487976755200, 9677996861569/16621994188800, 19820539601545337/34041844098662400. CROSSREFS Cf. A242597, A076788, A243456. Sequence in context: A147960 A155499 A321294 * A180807 A203455 A272582 Adjacent sequences:  A242593 A242594 A242595 * A242597 A242598 A242599 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Jun 16 2014 STATUS approved

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Last modified September 26 13:34 EDT 2021. Contains 347668 sequences. (Running on oeis4.)