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Decimal expansion of Sum_{k>=0} (2*k + 1)!/(3*k)!.
1

%I #12 Jun 07 2024 14:15:51

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

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

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

%N Decimal expansion of Sum_{k>=0} (2*k + 1)!/(3*k)!.

%F Equals hypergeometric([1, 3/2], [1/3, 2/3], 4/27).

%e 2.181344655134598339389148456673991324665...

%t s = Sum[ (2 k + 1)!/(3 k)!, {k, 0, Infinity}]

%t d = N[s, 100]

%t First[RealDigits[d]]

%t N[HypergeometricPFQ[{1, 3/2}, {1/3, 2/3}, 4/27], 100]

%o (PARI) suminf(k=0, (2*k + 1)!/(3*k)!) \\ _Michel Marcus_, Jun 01 2024

%Y Cf. A372776.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, May 31 2024