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

%I #9 Jul 03 2024 07:57:10

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

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

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

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

%F Equals (1/8)(10 + 7 e^(1/4) sqrt(Pi) erf(1/2)).

%F Equals 1F1(2;1/2;1/4) . - _R. J. Mathar_, Jul 03 2024

%e 2.2865189388213215074057263454433597027480...

%p hypergeom([2],[1/2],1/4) ; evalf(%) ; # _R. J. Mathar_, Jul 03 2024

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

%t d = N[s, 100]

%t First[RealDigits[d]]

%Y Cf. A371939.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Apr 27 2024