A381673 Decimal expansion of (720*e^7 - 4320*e^6 + 9000*e^5 - 7680*e^4 + 2430*e^3 - 192*e^2 + e) / 720.

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

Offset: 2

Author

Daniel Mondot, Mar 03 2025

Keywords

• nonn
• cons
• easy
• changed

Comments

Expected number of picks from a uniform [0,1] needed to first exceed a sum of 7.

Examples

			14.6666667815221434498094600315049...
		

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
• Index entries for transcendental numbers.

Crossrefs

Cf. A001113, A090142, A090143, A089139, A090611, A379601, A089087.

Programs

Mathematica

RealDigits[E^7 - 6*E^6 + 25*E^5/2 - 32*E^4/3 + 27*E^3/8 - 4*E^2/15 + E/720, 10, 120][[1]]

PARI

exp(7)-6*exp(6)+25*exp(5)-32*exp(4)/3+27*exp(3)/8-4*exp(2)/15+exp(1)/720

PARI

subst(Pol([1,-6,25/2,-32/3,27/8,-4/15,1/720,0]),x,exp(1)) \\ Charles R Greathouse IV, Aug 19 2025

Formula

Equals Sum_{k=0..n} (-1)^k * (n-k+1)^k * exp(n-k+1) / k! for n = 6 (Uspensky, 1937, p. 278).