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 A381673 #14 Aug 19 2025 11:35:41
%S A381673 1,4,6,6,6,6,6,6,7,8,1,5,2,2,1,4,3,4,4,9,8,0,9,4,6,0,0,3,1,5,0,4,9,4,
%T A381673 3,8,7,6,2,6,9,6,1,2,6,2,6,3,7,8,4,6,1,0,5,8,1,2,8,3,5,1,1,0,3,5,3,1,
%U A381673 4,1,3,1,0,0,4,1,9,8,8,6,0,2,7,1,9,4,3,9,5,9,7,4,1,5,9,6,8,7,0,1,4,3,8,9,4,3,7,7,0,7,6
%N A381673 Decimal expansion of (720*e^7 - 4320*e^6 + 9000*e^5 - 7680*e^4 + 2430*e^3 - 192*e^2 + e) / 720.
%C A381673 Expected number of picks from a uniform [0,1] needed to first exceed a sum of 7.
%D A381673 J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.
%H A381673 Daniel Mondot, <a href="/A381673/b381673.txt">Table of n, a(n) for n = 2..10001</a>
%H A381673 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%F A381673 Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 6 (Uspensky, 1937, p. 278).
%e A381673 14.6666667815221434498094600315049...
%t A381673 RealDigits[E^7 - 6*E^6 + 25*E^5/2 - 32*E^4/3 + 27*E^3/8 - 4*E^2/15 + E/720, 10, 120][[1]]
%o A381673 (PARI) exp(7)-6*exp(6)+25*exp(5)-32*exp(4)/3+27*exp(3)/8-4*exp(2)/15+exp(1)/720
%o A381673 (PARI) subst(Pol([1,-6,25/2,-32/3,27/8,-4/15,1/720,0]),x,exp(1)) \\ _Charles R Greathouse IV_, Aug 19 2025
%Y A381673 Cf. A001113, A090142, A090143, A089139, A090611, A379601, A089087.
%K A381673 nonn,cons,easy,changed
%O A381673 2,2
%A A381673 _Daniel Mondot_, Mar 03 2025