Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.
%I #22 May 19 2022 12:03:16
%S 0,9,4,5,7,3,0,1,9,6,6,4,7,6,1,9,3,9,5,1,3,5,8,8,9,0,0,8,5,4,4,1,3,8,
%T 4,9,3,1,4,9,5,5,3,2,9,3,1,9,2,2,4,0,1,0,4,9,7,9,5,1,5,3,1,9,5,5,5,9,
%U 2,1,0,2,7,5,4,7,6,6,3,1,1,2,8,9,7,7,4,0,1,4,8,4,9,0,9,9,6,5,1,5,2
%N Decimal expansion of Sum_{n>=1} n/sinh(n*Pi).
%C Prudnikov (p. 721, section 5.3.5, formula 1) has a typo, Gamma(1/4)^4 is correct, not Gamma(1/4)^2. - _Vaclav Kotesovec_, May 19 2022
%D A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series, Vol. 1 (Overseas Publishers Association, Amsterdam, 1986).
%F Gamma(1/4)^4/(32*Pi^3) - 1/(4*Pi).
%e 0.09457301966476193951358890085441384931495532931922401...
%t Join[{0}, RealDigits[Gamma[1/4]^4/(32*Pi^3) - 1/(4*Pi), 10, 100] // First]
%t N[EllipticK[k]/Pi^2*(EllipticK[k] - EllipticE[k]) /. k -> 1/2, 100] (* _Vaclav Kotesovec_, May 19 2022 *)
%o (PARI) suminf(k=1, k/sinh(k*Pi)) \\ _Vaclav Kotesovec_, May 19 2022
%o (PARI) suminf(k=1, 1/(2*sinh((k - 1/2)*Pi)^2)) \\ _Vaclav Kotesovec_, May 19 2022
%Y Cf. A068466, A335414, A335415.
%K nonn,cons,easy
%O 0,2
%A _Jean-François Alcover_, Aug 05 2014