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A379601 Decimal expansion of (120e^6 - 600e^5 + 960e^4 - 540e^3 + 80e^2 - e) / 120.

%I A379601 #33 Mar 23 2025 08:40:06
%S A379601 1,2,6,6,6,6,6,7,1,4,1,3,7,8,1,2,1,4,0,1,3,7,1,9,3,5,7,6,2,6,8,4,9,1,
%T A379601 1,1,9,5,6,4,7,4,3,7,0,7,7,7,4,0,1,9,6,7,5,6,7,1,0,5,3,7,5,5,6,8,2,6,
%U A379601 0,2,8,7,6,9,4,0,6,7,8,4,2,4,8,7,0,0,5,6,0,0,9,8,0,3,5,2,2,4,0,2,0,7,8,0,7,5,9,7,6,1,6
%N A379601 Decimal expansion of (120e^6 - 600e^5 + 960e^4 - 540e^3 + 80e^2 - e) / 120.
%C A379601 Expected number of picks from a uniform [0,1] needed to first exceed a sum of 6.
%D A379601 J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.
%H A379601 Daniel Mondot, <a href="/A379601/b379601.txt">Table of n, a(n) for n = 2..10001</a>
%H A379601 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UniformSumDistribution.html">Uniform Sum Distribution</a>.
%H A379601 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A379601 Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 5 (Uspensky, 1937, p. 278).
%e A379601 12.6666671413781214013719357626849111...
%t A379601 RealDigits[E^6 - 5*E^5 + 8*E^4 - 9*E^3/2 + 2*E^2/3 - E/120, 10, 120][[1]]
%o A379601 (PARI) exp(6)-5*exp(5)+8*exp(4)-9*exp(3)/2+2*exp(2)/3-exp(1)/120
%Y A379601 Cf. A001113, A090142, A090143, A089139, A090611, A381673, A089087.
%K A379601 nonn,cons,easy
%O A379601 2,2
%A A379601 _Daniel Mondot_, Feb 27 2025