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A303617 Decimal expansion of Sum_{k >= 0} 2^(2*k+1)/Product_{i = 0..k} (2*i+1). 0

%I #19 Apr 27 2018 17:08:35

%S 8,8,3,9,4,3,9,2,4,0,9,1,9,0,4,9,0,9,4,5,6,6,9,8,0,2,4,4,3,6,2,0,3,5,

%T 7,4,1,7,1,0,0,2,8,4,6,3,7,8,3,0,9,2,7,9,6,0,4,1,8,6,3,3,9,4,0,1,1,3,

%U 8,1,0,7,1,4,5,3,7,8,6,1,4,5,5,8,0,9,4,2,0,9,6,7,3

%N Decimal expansion of Sum_{k >= 0} 2^(2*k+1)/Product_{i = 0..k} (2*i+1).

%F Equals e^2*sqrt(Pi/2)*erf(sqrt(2)) = A072334*A069998*A110894.

%e 8.83943924091904909456698024436203574171002846378309279604186339401138107...

%e 2/1 + 2^3/(1*3) + 2^5/(1*3*5) + 2^7/(1*3*5*7) + 2^9/(1*3*5*7*9) + 2^11/(1*3*5*7*9*11) + 2^13/(1*3*5*7*9*11*13) + ...

%t RealDigits[E^2 Sqrt[Pi/2] Erf[Sqrt[2]], 10, 100][[1]]

%o (PARI) suminf(k=0, 2^(2*k+1)/prod(i=0, k, (2*i+1))) \\ _Michel Marcus_, Apr 27 2018

%Y Cf. A001147, A004171.

%Y Cf. A069998, A072334, A110894.

%K nonn,cons

%O 1,1

%A _Bruno Berselli_, Apr 27 2018

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Last modified April 19 16:21 EDT 2024. Contains 371794 sequences. (Running on oeis4.)