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

0,2

Links

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

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

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);

Crossrefs

Column k=8 of A292804.

Sequence in context: A155615 A322650 A221765 * A133271 A180903 A266427

Adjacent sequences: A292839 A292840 A292841 * A292843 A292844 A292845

Keyword

nonn

Author

Alois P. Heinz, Sep 24 2017

Status

approved