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 A268086 Decimal expansion of Sum_{k>0} 1/(k*((k+1)^2+1)). 3
 2, 9, 7, 5, 9, 5, 9, 6, 9, 0, 2, 7, 7, 1, 4, 3, 3, 1, 8, 7, 2, 1, 6, 9, 8, 8, 9, 0, 2, 7, 1, 5, 6, 3, 3, 1, 5, 3, 6, 3, 8, 3, 0, 2, 0, 6, 4, 9, 8, 2, 4, 2, 7, 8, 2, 3, 1, 8, 4, 7, 2, 3, 7, 3, 0, 6, 8, 0, 9, 2, 9, 6, 8, 0, 9, 3, 1, 7, 6, 5, 1, 2, 8, 8, 4, 2, 6, 1, 1, 0, 5, 1, 3, 9, 0, 2, 4, 6, 4, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Also, decimal expansion of Integral_{x=0..1} (2 - (1-i)*x^(1-i) - (1+i)*x^(1+i))/(4 - 4*x) dx, where i is the imaginary unit. LINKS Table of n, a(n) for n=0..99. FORMULA Equals (1 - i)*(H(1-i) + i*H(1+i))/4, where H(z) is a harmonic number with complex argument. Equals (Psi(i-1)-Psi(1)-i+1)/2-Pi*(i+1)*coth(Pi)/4), where Psi(x) is the digamma function. - Peter Luschny, Jan 27 2016 EXAMPLE .297595969027714331872169889027156331536383020649824278231847237306809... MAPLE ((1-I)*(harmonic(1-I) + I*harmonic(1+I)))/4: Re(evalf(%, 106)); # Peter Luschny, Jan 27 2016 MATHEMATICA (1 - I)*(HarmonicNumber[1 - I] + I*HarmonicNumber[1 + I])/4 // Re // RealDigits[#, 10, 100]& // First (* Jean-François Alcover, Jan 26 2016 *) PROG (Sage) # Warning: Floating point calculation. Adjust precision as needed # and use some guard digits! from mpmath import mp, chop, psi, coth, pi mp.dps = 108; mp.pretty = True chop((psi(0, I-1)-psi(0, 1)-I+1)/2-pi*(I+1)*coth(pi)/4) # Peter Luschny, Jan 27 2016 CROSSREFS Cf. A062158: numbers of the form k*((k+1)^2+1), with k>-2. Cf. A268046: (1+i)*(H(1-i)-i*H(1+i))/4. Sequence in context: A176977 A202473 A180310 * A021340 A241753 A157350 Adjacent sequences: A268083 A268084 A268085 * A268087 A268088 A268089 KEYWORD nonn,cons AUTHOR Bruno Berselli, Jan 26 2016 STATUS approved

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Last modified September 23 02:06 EDT 2023. Contains 365532 sequences. (Running on oeis4.)