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%I #7 Oct 11 2023 08:41:32
%S 1,31031,1346704211,15166600495229,2769520712100913771,
%T 14140406602762826441989,733773840666057086093759257,
%U 2827389271155038104266471538091,4190504590060194179938375947107323897
%N Numerators of probabilities in the Newton-Pepys problem.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Newton-PepysProblem.html">Newton-Pepys Problem</a>
%F (5^(5*n)*(6*n)!*Hypergeometric2F1Regularized[1, -5*n, 1 + n, -1/5])/(6^(6*n)*(5*n)!)
%e 1, 31031/46656, 1346704211/2176782336, 15166600495229/25389989167104, ...
%t Numerator[Table[5^(5 n) (6 n)! Hypergeometric2F1Regularized[1, -5 n, n + 1, -1/5]/(6^(6 n) (5 n)!), {n, 0, 20}]]
%Y Cf. A143163.
%K nonn,frac
%O 0,2
%A _Eric W. Weisstein_, Jul 27 2008