A292843 Number of sets of nonempty words with a total of n letters over 9-ary alphabet.

1, 9, 117, 1542, 19404, 239481, 2900802, 34609797, 407615175, 4747112731, 54743025339, 625791326688, 7097863351275, 79938092898747, 894514969436076, 9951032414168964, 110103625982603466, 1212181195307220126, 13283829023674846878, 144946503880942833774

Offset: 0

Author

Alois P. Heinz, Sep 24 2017

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Column k=9 of A292804.

Programs

Maple

h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))
    end:
a:= n-> h(n$2):
seq(a(n), n=0..30);

Formula

G.f.: Product_{j>=1} (1+x^j)^(9^j).

a(n) ~ 9^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(9^(m-1)-1)) = 0.058648829660552563553047659756831342987... - Vaclav Kotesovec, Sep 28 2017