A382020 Decimal expansion of (5040*e^8 - 35280*e^7 + 90720*e^6 - 105000*e^5 + 53760*e^4 - 10206*e^3 + 448*e^2 - e) / 5040.

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

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 8.

Examples

			16.6666666704268878236623470...
		

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, A381843, A382026, A089087.

Programs

Mathematica

RealDigits[E^8 - 7*E^7 + 18*E^6 - 125*E^5/6 + 32*E^4/3 - 81*E^3/40 + 4*E^2/45 - E/5040, 10, 120][[1]]

PARI

exp(8)-7*exp(7)+18*exp(6)-125*exp(5)/6+32*exp(4)/3-81*exp(3)/40+4*exp(2)/45-exp(1)/5040

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 7 (Uspensky, 1937, p. 278).