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%I #18 Aug 13 2020 08:56:54
%S 1,6,4,1,6,3,2,5,6,0,6,5,5,1,5,3,8,6,6,2,9,3,8,4,2,7,7,0,2,2,5,4,2,9,
%T 4,3,4,2,2,6,0,6,1,5,3,7,9,5,6,7,3,9,7,4,7,8,0,4,6,5,1,6,2,2,3,8,0,1,
%U 4,4,6,0,3,7,3,3,3,5,1,7,7,5,6,0,0,3,6,4,1,7,1,6,2,3,3,5,9
%N Decimal expansion of Sum_{k>=0} 1/2^(k*(k+1)/2).
%C The binary expansion is the characteristic function A010054 of the triangular numbers A000217.
%F Equals 1 + A190405 (as a decimal number).
%F Equals Product{k>=1} (1 - 1/2^(2*k))/(1 - 1/2^(2*k-1)). - _Amiram Eldar_, Aug 13 2020
%e 1.641632560655153866293842770225429434226061537956739747804651622380144603733...
%t RealDigits[QPochhammer[1/4, 1/4]/QPochhammer[2, 1/4], 10, 100][[1]] (* _Amiram Eldar_, Aug 13 2020 *)
%o (PARI) default(realprecision,200);suminf(k=0,2^(-k*(k+1)/2))
%Y Cf. A000217, A010054, A190405, A333797.
%K nonn,cons
%O 1,2
%A _M. F. Hasler_, Feb 27 2018
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