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Decimal expansion of Sum_{k>=0} (-1)^k (k+1)! / (2k)!.
1

%I #9 Aug 27 2024 09:57:44

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

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

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

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

%F Equals (6 e^(1/4) - 5 Sqrt(Pi) erfi(1/2))/(8 e^(1/4)).

%F Equals 1F1(2;1/2;-1/4). - _R. J. Mathar_, Aug 27 2024

%e 0.219454520622472130082447059387913036129463153300...

%t s = Sum[(-1)^k (k + 1)!/(2 k)!, {k, 0, Infinity}]

%t d = N[s, 100]

%t First[RealDigits[d]]

%Y Cf. A371937.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Apr 27 2024