A090611 Decimal expansion of (24*e^5 - 96*e^4 + 108*e^3 - 32*e^2 + e)/24.

1, 0, 6, 6, 6, 6, 6, 2, 0, 6, 8, 6, 2, 2, 4, 1, 1, 8, 5, 8, 0, 1, 9, 0, 2, 7, 3, 7, 1, 9, 3, 2, 8, 4, 7, 0, 6, 8, 6, 0, 3, 1, 0, 2, 5, 8, 1, 0, 8, 4, 7, 5, 8, 3, 4, 3, 3, 2, 5, 7, 9, 3, 1, 9, 8, 1, 3, 3, 9, 6, 1, 0, 0, 4, 1, 2, 1, 6, 3, 4, 0, 7, 5, 3, 2, 8, 7, 8, 2, 0, 4, 3, 9, 2, 5, 0, 5, 0, 4, 3, 7, 9, 5, 8, 7

Offset: 2

Author

Ray Chandler, Dec 07 2003

Keywords

• nonn
• cons
• easy

Comments

Expected number of picks from a uniform [0,1] needed to first exceed a sum of 5.

Examples

			10.66666206862241185801902737193284706860310258108475834332579319813396100412163407...
		

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, A379601, A381673, A382020, A381843, A382026, A090137, A090138, A089087.

Programs

Mathematica

RealDigits[E^5 - 4*E^4 + 9*E^3/2 - 4*E^2/3 + E/24, 10, 120][[1]] (* Amiram Eldar, Jun 20 2023 *)

PARI

exp(5)-4*exp(4)+9*exp(3)/2-4*exp(2)/3+exp(1)/24

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 4 (Uspensky, 1937, p. 278).

Extensions

Offset corrected by R. J. Mathar, Feb 05 2009