This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382020 #18 Mar 23 2025 05:31:40
%S A382020 1,6,6,6,6,6,6,6,6,7,0,4,2,6,8,8,7,8,2,3,6,6,2,3,4,7,0,0,4,3,3,2,5,8,
%T A382020 0,4,4,9,3,6,4,9,5,7,7,5,8,9,7,0,2,0,7,0,7,8,7,1,2,8,4,1,5,7,6,3,7,6,
%U A382020 1,8,5,7,5,9,4,9,7,2,1,4,6,2,7,6,4,6,6,0
%N A382020 Decimal expansion of (5040*e^8 - 35280*e^7 + 90720*e^6 - 105000*e^5 + 53760*e^4 - 10206*e^3 + 448*e^2 - e) / 5040.
%C A382020 Expected number of picks from a uniform [0,1] distribution needed to first exceed a sum of 8.
%D A382020 J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.
%H A382020 Daniel Mondot, <a href="/A382020/b382020.txt">Table of n, a(n) for n = 2..10001</a>
%F A382020 Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 7 (Uspensky, 1937, p. 278).
%e A382020 16.6666666704268878236623470...
%t A382020 RealDigits[E^8 - 7*E^7 + 18*E^6 - 125*E^5/6 + 32*E^4/3 - 81*E^3/40 + 4*E^2/45 - E/5040, 10, 120][[1]]
%o A382020 (PARI) exp(8)-7*exp(7)+18*exp(6)-125*exp(5)/6+32*exp(4)/3-81*exp(3)/40+4*exp(2)/45-exp(1)/5040
%Y A382020 Cf. A001113, A090142, A090143, A089139, A090611, A379601, A381673, A381843, A382026, A089087.
%K A382020 nonn,cons,easy
%O A382020 2,2
%A A382020 _Daniel Mondot_, Mar 12 2025