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%I #16 Apr 06 2024 09:03:11
%S 2,2,10,122,2770,101042,5405530,398721962,38783024290,4809759350882,
%T 740742376475050,138697748786275802,31029068327114173810,
%U 8174145018586247784722,2504519282807259730936570,883087786498046209107365642,355038783159078578873329579330,161446598471775796124336494906562
%N Twice A000364.
%H G. Almkvist, <a href="http://www.jstor.org/stable/2974583">Many correct digits of Pi, revisited</a>, Amer. Math. Monthly, 104 (1997), 351-353.
%H J. M. Borwein, <a href="https://carmamaths.org/resources/jon/OEIStalk.pdf">Adventures with the OEIS: Five sequences Tony may like</a>, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
%H J. M. Borwein, <a href="/A060997/a060997.pdf">Adventures with the OEIS: Five sequences Tony may like</a>, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]
%F E.g.f.: 2 - 2/Q(0), where Q(k)= 1 - (2*k+1)*(2*k+2)/x + 1/x*(2*k+1)*(2*k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, May 01 2013
%F From _Peter Luschny_, Aug 18 2021: (Start)
%F a(n) = (-1)^n*4^(2*n+1)*(Bernoulli(2*n+1, 3/4) - Bernoulli(2*n+1, 1/4))/(2*n+1).
%F a(n) = (-1)^n*4*Im(PolyLog(-2*n, i)). (End)
%t a[n_] := (-1)^n 4 Im[PolyLog[-2 n, I]];
%t Table[a[n], {n, 0, 17}] (* _Peter Luschny_, Aug 18 2021 *)
%Y Cf. A000364, A009752.
%K nonn
%O 0,1
%A _N. J. A. Sloane_
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