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%I #10 May 03 2024 20:47:23
%S 2,3,1,2,4,4,9,4,4,4,2,4,8,6,5,5,1,3,8,5,4,4,6,5,7,5,4,0,3,2,7,2,0,0,
%T 2,0,1,0,9,8,9,0,8,9,9,5,4,4,8,6,8,8,5,7,3,3,4,1,7,2,6,9,3,9,8,8,8,1,
%U 0,2,3,4,0,2,6,8,6,0,8,4,8,9,3,1,1,9,4,8,5,5,6
%N Decimal expansion of Sum_{k>=1} sqrt(k)*exp(-k/2).
%H Tim van de Brug, Wouter Kager, and Ronald Meester, <a href="https://research.vu.nl/ws/portalfiles/portal/282858399/MPRF23_35-66_The_Asymptotics_of_Group_Russian_Roulette.pdf">The asymptotics of group Russian roulette</a>, Markov Processes and Related Fields, Vol. 23, No. 1 (2017), pp. 35-66; <a href="https://arxiv.org/abs/1507.03805">arXiv preprint</a>, arXiv:1507.03805 [math.PR], 1 May 2017, page 10, (2.19).
%e 2.3124494442486551385446575403272002010989089954486885733417269398881...
%t RealDigits[PolyLog[-1/2, 1/Sqrt[E]], 10, 120][[1]] (* _Amiram Eldar_, May 03 2024 *)
%o (PARI) suminf(k=1,sqrt(k)*exp(-k/2))
%K nonn,cons
%O 1,1
%A _Hugo Pfoertner_, May 03 2024