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 A382026 #13 Mar 23 2025 05:28:26
%S A382026 2,0,6,6,6,6,6,6,6,6,6,4,7,6,3,1,8,8,0,0,6,1,4,1,6,3,0,9,1,0,5,9,7,6,
%T A382026 6,4,6,8,6,5,6,8,6,0,8,2,1,5,4,4,7,4,2,3,8,4,1,9,2,0,9,0,6,0,0,0,7,3,
%U A382026 8,5,3,6,8,8,3,6,1,5,8,9,8,2,5,8,2,3,4,5
%N A382026 Decimal expansion of (362880*e^10 - 3265920*e^9 + 11612160*e^8 - 20744640*e^7 + 19595520*e^6 - 9450000*e^5 + 2064384*e^4 - 157464*e^3 + 2304*e^2 - e) / 362880.
%C A382026 Expected number of picks from a uniform [0,1] distribution needed to first exceed a sum of 10.
%D A382026 J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.
%H A382026 Daniel Mondot, <a href="/A382026/b382026.txt">Table of n, a(n) for n = 2..10001</a>
%F A382026 Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 9 (Uspensky, 1937, p. 278).
%e A382026 20.666666666476318800614163...
%t A382026 RealDigits[E^10 - 9*E^9 + 32*E^8 - 343*E^7/6 + 54*E^6 - 625*E^5/24 + 256*E^4/45 - 243*E^3/560 + 2*E^2/315 - E/362880, 10, 120][[1]]
%o A382026 (PARI) exp(10)-9*exp(9)+32*exp(8)-343*exp(7)/6+54*exp(6)-625*exp(5)/24+256*exp(4)/45-243*exp(3)/560+2*exp(2)/315-exp(1)/362880
%Y A382026 Cf. A001113, A090142, A090143, A089139, A090611, A379601, A381673, A382020, A381843, A089087.
%K A382026 nonn,cons,easy
%O A382026 2,1
%A A382026 _Daniel Mondot_, Mar 12 2025