|
|
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.
|
|
4
|
|
|
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 612579511, 5738374621, 53509541320, 496353364300, 4576113154000, 41886926650000, 380127217600000, 3413851687000000, 30264311980000000, 263901070900000000, 2401684855296999121, 21793684651236981541, 197206153848009709930
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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
|
|
EXAMPLE
|
1/9, 10/81, 100/729, 1000/6561, 10000/59049, ...
|
|
MATHEMATICA
|
Table[Numerator@ SeriesCoefficient[(1 - x^9)/(x^10 - 10 x + 9), {x, 0, n}], {n, 0, 21}]
|
|
PROG
|
(PARI) s = Vec(Ser((1-x^9)/(x^10-10*x+9), x, 666));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,frac,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|