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

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, 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, 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

Offset: 2

Author

Daniel Mondot, Feb 27 2025

Keywords

• nonn
• cons
• easy

Comments

Expected number of picks from a uniform [0,1] needed to first exceed a sum of 6.

Examples

			12.6666671413781214013719357626849111...
		

References

• J. V. Uspensky, Introduction to Mathematical Probability, New York: McGraw-Hill, 1937.

Links

• Daniel Mondot, Table of n, a(n) for n = 2..10001
• Eric Weisstein's World of Mathematics, Uniform Sum Distribution.
• Index entries for transcendental numbers.

Crossrefs

Cf. A001113, A090142, A090143, A089139, A090611, A381673, A089087.

Programs

Mathematica

RealDigits[E^6 - 5*E^5 + 8*E^4 - 9*E^3/2 + 2*E^2/3 - E/120, 10, 120][[1]]

PARI

exp(6)-5*exp(5)+8*exp(4)-9*exp(3)/2+2*exp(2)/3-exp(1)/120

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 5 (Uspensky, 1937, p. 278).