A292841 - OEIS

%I #7 Sep 28 2017 04:29:07

%S 1,7,70,721,7042,67592,636517,5904746,54072137,489655873,4390760297,

%T 39030158111,344244293260,3014869505704,26235190722937,

%U 226961433002801,1952889252127030,16720135949099562,142493658202081151,1209158776638832488,10219419639669800154

%N Number of sets of nonempty words with a total of n letters over 7-ary alphabet.

%H Alois P. Heinz, <a href="/A292841/b292841.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: Product_{j>=1} (1+x^j)^(7^j).

%F a(n) ~ 7^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(7^(m-1)-1)) = 0.07704538722753681799661640414751144459... - _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(7^i, j), j=0..n/i)))

%p     end:

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

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

%Y Column k=7 of A292804.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Sep 24 2017