cp's OEIS Frontend

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

%I A292842 #7 Sep 28 2017 04:29:57
%S A292842 1,8,92,1080,12070,132408,1425372,15114504,158210353,1637612160,
%T A292842 16784647360,170537275776,1719204122528,17209440777600,
%U A292842 171165585295552,1692447401221248,16644429470981928,162875924564677824,1586486181338263456,15386713233832145728
%N A292842 Number of sets of nonempty words with a total of n letters over 8-ary alphabet.
%H A292842 Alois P. Heinz, <a href="/A292842/b292842.txt">Table of n, a(n) for n = 0..1000</a>
%F A292842 G.f.: Product_{j>=1} (1+x^j)^(8^j).
%F A292842 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
%p A292842 h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A292842       add(h(n-i*j, i-1)*binomial(8^i, j), j=0..n/i)))
%p A292842     end:
%p A292842 a:= n-> h(n$2):
%p A292842 seq(a(n), n=0..30);
%Y A292842 Column k=8 of A292804.
%K A292842 nonn
%O A292842 0,2
%A A292842 _Alois P. Heinz_, Sep 24 2017