A292843 - OEIS

%I #7 Sep 28 2017 04:30:49

%S 1,9,117,1542,19404,239481,2900802,34609797,407615175,4747112731,

%T 54743025339,625791326688,7097863351275,79938092898747,

%U 894514969436076,9951032414168964,110103625982603466,1212181195307220126,13283829023674846878,144946503880942833774

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

%H Alois P. Heinz, <a href="/A292843/b292843.txt">Table of n, a(n) for n = 0..1000</a>

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

%F 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

%p h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p       add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))

%p     end:

%p a:= n-> h(n$2):

%p seq(a(n), n=0..30);

%Y Column k=9 of A292804.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 24 2017