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.

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

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 9.

Examples

			18.66666666527032134895552...
		

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, A382026, A089087.

Programs

Mathematica

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]]

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

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 8 (Uspensky, 1937, p. 278).