A292842 Number of sets of nonempty words with a total of n letters over 8-ary alphabet.

1, 8, 92, 1080, 12070, 132408, 1425372, 15114504, 158210353, 1637612160, 16784647360, 170537275776, 1719204122528, 17209440777600, 171165585295552, 1692447401221248, 16644429470981928, 162875924564677824, 1586486181338263456, 15386713233832145728

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=8 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(8^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)^(8^j).

a(n) ~ 8^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(8^(m-1)-1)) = 0.066582557989772785055691589503818396917... - Vaclav Kotesovec, Sep 28 2017