cp's OEIS Frontend

A292840 Number of sets of nonempty words with a total of n letters over 6-ary alphabet.

%I A292840 #9 Sep 28 2017 04:28:10
%S A292840 1,6,51,452,3777,31074,250735,1993176,15640983,121378650,932738805,
%T A292840 7105552308,53709133137,403124780178,3006420386499,22290321581448,
%U A292840 164378277308862,1206180958964508,8810022165617086,64073173243207632,464122836576398454,3349321050668452460
%N A292840 Number of sets of nonempty words with a total of n letters over 6-ary alphabet.
%H A292840 Alois P. Heinz, <a href="/A292840/b292840.txt">Table of n, a(n) for n = 0..1000</a>
%F A292840 G.f.: Product_{j>=1} (1+x^j)^(6^j).
%F A292840 a(n) ~ 6^n * exp(2*sqrt(n) - 1/2 - c) / (2 * sqrt(Pi) * n^(3/4)), where c = Sum_{m>=2} (-1)^m/(m*(6^(m-1)-1)) = 0.091503304254691843343610606469481430508... - _Vaclav Kotesovec_, Sep 28 2017
%p A292840 h:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A292840       add(h(n-i*j, i-1)*binomial(6^i, j), j=0..n/i)))
%p A292840     end:
%p A292840 a:= n-> h(n$2):
%p A292840 seq(a(n), n=0..30);
%Y A292840 Column k=6 of A292804.
%K A292840 nonn
%O A292840 0,2
%A A292840 _Alois P. Heinz_, Sep 24 2017