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.

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

Offset: 2

Author

Daniel Mondot, Mar 12 2025

Keywords

• nonn
• cons
• easy

Comments

Expected number of picks from a uniform [0,1] distribution needed to first exceed a sum of 10.

Examples

			20.666666666476318800614163...
		

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

Crossrefs

Cf. A001113, A090142, A090143, A089139, A090611, A379601, A381673, A382020, A381843, A089087.

Programs

Mathematica

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]]

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

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 9 (Uspensky, 1937, p. 278).