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

%I #10 Jun 07 2024 14:16:00

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

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

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

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

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

%e 1.088300303254427561687202908353381908685907755580814880...

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

%t d = N[s, 100]

%t First[RealDigits[d]]

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

%o (PARI) suminf(k=0, (2*k)!/(3*k + 1)!) \\ ~~~é

%Y Cf. A372775.

%K nonn,cons

%O 1,3

%A _Clark Kimberling_, May 31 2024