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 A242376 Numerators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0. 4
 0, 1, 1, 5, 1, 4, 13, 151, 16, 83, 73, 1433, 647, 15341, 28211, 10447, 608, 19345, 18181, 651745, 771079, 731957, 2786599, 122289917, 14614772, 140001721, 134354573, 774885169, 745984697, 41711914513, 80530073893, 4825521853483 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS See the denominators in A241519. b(n) = 0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ... (Ta0(n) in A241269) is an autosequence of the first kind. LINKS Ralf Stephan, Table of n, a(n) for n = 0..999 FORMULA 0 = b(n)*(+b(n+1) - 4*b(n+2) + 4*b(n+3)) + b(n+1)*(-2*b(n+1) + 9*b(n+2) - 10*b(n+3)) + b(n+2)*(-2*b(n+2) + 4*b(n+3)) if n>=0. - Michael Somos, May 26 2014 b(n) = -Re(Phi(2, 1, n + 1)). - Eric W. Weisstein, Dec 11 2017 G.f. for b(n): -log(1-x)/(2*(1-x/2)). - Vladimir Kruchinin, Nov 14 2022 EXAMPLE 0, 1/2, 1/2, 5/12, 1/3, 4/15, 13/60, 151/840, 16/105, 83/630, 73/630, ... MATHEMATICA Table[-Re[LerchPhi[2, 1, n + 1]], {n, 0, 20}] // Numerator (* Eric W. Weisstein, Dec 11 2017 *) -Re[LerchPhi[2, 1, Range[20]]] // Numerator (* Eric W. Weisstein, Dec 11 2017 *) RecurrenceTable[{b[n] == b[n - 1]/2 + 1/(2 n), b[0] == 0}, b[n], {n, 20}] // Numerator (* Eric W. Weisstein, Dec 11 2017 *) PROG (Sage) def a(): b = n = 0 while True: yield numerator(b) n = n + 1 b = (b/2 + 1/(2*n)) # Ralf Stephan, May 18 2014 CROSSREFS Cf. A241519 (denominators). Sequence in context: A316248 A180132 A286593 * A307393 A231923 A105664 Adjacent sequences: A242373 A242374 A242375 * A242377 A242378 A242379 KEYWORD nonn,frac AUTHOR Paul Curtz, May 12 2014 EXTENSIONS a(14)-a(25) from Jean-François Alcover, May 12 2014 Corrected a(22) and a(24), more terms from Ralf Stephan, May 18 2014 STATUS approved

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Last modified May 18 16:58 EDT 2024. Contains 372664 sequences. (Running on oeis4.)