A100061 Numerator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 612579511, 5738374621, 53509541320, 496353364300, 4576113154000, 41886926650000, 380127217600000, 3413851687000000, 30264311980000000, 263901070900000000, 2401684855296999121, 21793684651236981541, 197206153848009709930
Offset: 1
Examples
1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
Links
- Stanislav Sykora, Table of n, a(n) for n = 1..666
- Eric Weisstein's World of Mathematics, Evil Number
Programs
-
Mathematica
Table[Numerator@ SeriesCoefficient[(1 - x^9)/(x^10 - 10 x + 9), {x, 0, n}], {n, 0, 21}] -
PARI
s = Vec(Ser((1-x^9)/(x^10-10*x+9),x,666)); a = vector(#s,n,numerator(s[n])) \\ Stanislav Sykora, Apr 16 2016
Formula
Empirical g.f.: x * (1 +9*x +81*x^2) * (1 +729*x^3 +531441*x^6) / ((1 -9*x) * (1 +8*x +63*x^2 +486*x^3 +3645*x^4 +26244*x^5 +177147*x^6 +1062882*x^7 +4782969*x^8)). - Colin Barker, Apr 17 2016
Extensions
More terms from Michael De Vlieger, Apr 16 2016