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

%I #9 Jun 07 2024 14:15:27

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

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

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

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

%F HypergeometricPFQ((1,3/2),(2/3,4/3),-4/27).

%e 0.772477052213696364357836702455607205794658...

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

%t d = N[s, 100]

%t First[RealDigits[d]]

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

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

%Y Cf. A372773.

%K cons,nonn

%O 0,1

%A _Clark Kimberling_, May 31 2024