A011248 Twice A000364.

2, 2, 10, 122, 2770, 101042, 5405530, 398721962, 38783024290, 4809759350882, 740742376475050, 138697748786275802, 31029068327114173810, 8174145018586247784722, 2504519282807259730936570, 883087786498046209107365642, 355038783159078578873329579330, 161446598471775796124336494906562

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• G. Almkvist, Many correct digits of Pi, revisited, Amer. Math. Monthly, 104 (1997), 351-353.
• J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016.
• J. M. Borwein, Adventures with the OEIS: Five sequences Tony may like, Guttmann 70th [Birthday] Meeting, 2015, revised May 2016. [Cached copy, with permission]

Crossrefs

Cf. A000364, A009752.

Programs

Mathematica

a[n_] := (-1)^n 4 Im[PolyLog[-2 n, I]];
Table[a[n], {n, 0, 17}] (* Peter Luschny, Aug 18 2021 *)

Formula

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

From Peter Luschny, Aug 18 2021: (Start)

a(n) = (-1)^n*4^(2*n+1)*(Bernoulli(2*n+1, 3/4) - Bernoulli(2*n+1, 1/4))/(2*n+1).

a(n) = (-1)^n*4*Im(PolyLog(-2*n, i)). (End)