cp's OEIS Frontend

A381843 Decimal expansion of (40320*e^9 - 322560*e^8 + 987840*e^7 - 1451520*e^6 + 1050000*e^5 - 344064*e^4 + 40824*e^3 - 1024*e^2 + e) / 40320.

%I A381843 #30 Mar 23 2025 05:29:15
%S A381843 1,8,6,6,6,6,6,6,6,6,5,2,7,0,3,2,1,3,4,8,9,5,5,5,2,1,7,2,2,9,4,8,5,6,
%T A381843 9,6,1,0,0,2,7,8,4,8,3,5,6,2,1,5,5,0,7,6,9,8,4,1,6,0,8,4,6,7,9,9,2,7,
%U A381843 1,6,2,2,2,5,3,5,9,5,2,6,2,6,5,8,1,1,3
%N A381843 Decimal expansion of (40320*e^9 - 322560*e^8 + 987840*e^7 - 1451520*e^6 + 1050000*e^5 - 344064*e^4 + 40824*e^3 - 1024*e^2 + e) / 40320.
%C A381843 Expected number of picks from a uniform [0,1] distribution needed to first exceed a sum of 9.
%D A381843 J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.
%H A381843 Daniel Mondot, <a href="/A381843/b381843.txt">Table of n, a(n) for n = 2..10001</a>
%F A381843 Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 8 (Uspensky, 1937, p. 278).
%e A381843 18.66666666527032134895552...
%t A381843 RealDigits[E^9 - 8*E^8 + 49*E^7/2 - 36*E^6 + 625*E^5/24 - 128*E^4/15 + 81*E^3/80 - 8*E^2/315 + E/40320, 10, 120][[1]]
%o A381843 (PARI) exp(9)-8*exp(8)+49*exp(7)/2-36*exp(6)+625*exp(5)/24-128*exp(4)/15+81*exp(3)/80-8*exp(2)/315+exp(1)/40320
%Y A381843 Cf. A001113, A090142, A090143, A089139, A090611, A379601, A381673, A382020, A382026, A089087.
%K A381843 nonn,cons,easy
%O A381843 2,2
%A A381843 _Daniel Mondot_, Mar 12 2025