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A292841 Number of sets of nonempty words with a total of n letters over 7-ary alphabet.

%I A292841 #7 Sep 28 2017 04:29:07
%S A292841 1,7,70,721,7042,67592,636517,5904746,54072137,489655873,4390760297,
%T A292841 39030158111,344244293260,3014869505704,26235190722937,
%U A292841 226961433002801,1952889252127030,16720135949099562,142493658202081151,1209158776638832488,10219419639669800154
%N A292841 Number of sets of nonempty words with a total of n letters over 7-ary alphabet.
%H A292841 Alois P. Heinz, <a href="/A292841/b292841.txt">Table of n, a(n) for n = 0..1000</a>
%F A292841 G.f.: Product_{j>=1} (1+x^j)^(7^j).
%F A292841 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 A292841 h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A292841       add(h(n-i*j, i-1)*binomial(7^i, j), j=0..n/i)))
%p A292841     end:
%p A292841 a:= n-> h(n$2):
%p A292841 seq(a(n), n=0..30);
%Y A292841 Column k=7 of A292804.
%K A292841 nonn
%O A292841 0,2
%A A292841 _Alois P. Heinz_, Sep 24 2017