cp's OEIS Frontend

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

%I A292843 #7 Sep 28 2017 04:30:49
%S A292843 1,9,117,1542,19404,239481,2900802,34609797,407615175,4747112731,
%T A292843 54743025339,625791326688,7097863351275,79938092898747,
%U A292843 894514969436076,9951032414168964,110103625982603466,1212181195307220126,13283829023674846878,144946503880942833774
%N A292843 Number of sets of nonempty words with a total of n letters over 9-ary alphabet.
%H A292843 Alois P. Heinz, <a href="/A292843/b292843.txt">Table of n, a(n) for n = 0..1000</a>
%F A292843 G.f.: Product_{j>=1} (1+x^j)^(9^j).
%F A292843 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 A292843 h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A292843       add(h(n-i*j, i-1)*binomial(9^i, j), j=0..n/i)))
%p A292843     end:
%p A292843 a:= n-> h(n$2):
%p A292843 seq(a(n), n=0..30);
%Y A292843 Column k=9 of A292804.
%K A292843 nonn
%O A292843 0,2
%A A292843 _Alois P. Heinz_, Sep 24 2017