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%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