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

1,2

Links

Stanislav Sykora, Table of n, a(n) for n = 1..666

Eric Weisstein's World of Mathematics, Evil Number

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));
a = vector(#s, n, numerator(s[n])) \\ Stanislav Sykora, Apr 16 2016

Crossrefs

Cf. A100062.

Cf. A271880, A271881.

Sequence in context: A232662 A168070 A263019 * A125858 A086067 A348783

Adjacent sequences: A100058 A100059 A100060 * A100062 A100063 A100064

Keyword

nonn,base,frac,easy

Author

Eric W. Weisstein, Nov 01 2004

Extensions

More terms from Michael De Vlieger, Apr 16 2016

Status

approved