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A261315 Number of n-digit positive numbers whose digits occur with equal frequency. 2
9, 90, 657, 4788, 27225, 146619, 544329, 2112084, 3447369, 28995255, 9, 1488185631, 9, 73556822205, 38222232057, 3321970172244, 9, 138479121435807, 9, 2209806802214163, 19711054740199689, 28570005, 9, 15574715941421647071, 141378216540777225, 421224309, 9724427617362202602009 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

a(n) is divisible by 9.

a(n) = 9 if n > 10 is prime.

LINKS

Robert Israel, Table of n, a(n) for n = 1..919

FORMULA

a(n) = (9/10) * Sum_{j | n, j <= 10} n! * ((n/j)!)^(-j) * binomial(10,j).

EXAMPLE

For n = 1 there are the numbers 1 to 9.

For n = 2 there are 9 two-digit numbers of the form dd and 81 with two distinct digits, for a total of 90.

For n = 3 there are 9 numbers of the form ddd and 648 with three distinct digits, for a total of 657.

For n = 4 there are 9 numbers of the form dddd, 243 of with two distinct digits each occurring twice, and 4536 with four distinct digits, for a total of 4788.

MAPLE

seq(9/10*add(n!/(n/j)!^j * binomial(10, j), j = select(`<=`, numtheory:-divisors(n), 10)), n=1..30);

CROSSREFS

Cf. A052060.

Sequence in context: A277105 A180289 A210088 * A270242 A054616 A052386

Adjacent sequences:  A261312 A261313 A261314 * A261316 A261317 A261318

KEYWORD

nonn,base

AUTHOR

Robert Israel, Aug 14 2015

STATUS

approved

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)