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A194721 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting nine doublets into the initially empty word.

%I A194721 #9 Jul 13 2015 19:09:14
%S A194721 0,1,24310,2699837,52955950,464221105,2561439806,10466643805,
%T A194721 34648845862,98156060225,246643289830,563506356061,1191627482750,
%U A194721 2363434581937,4441172224750,7969478316605,13742556531766,22888430598145,36972962559062,58126513174525,89196318660430
%N A194721 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting nine doublets into the initially empty word.
%H A194721 Alois P. Heinz, <a href="/A194721/b194721.txt">Table of n, a(n) for n = 0..1000</a>
%F A194721 G.f.: -x * (1 +24301*x +2481083*x^2 +29532493*x^3 +82769773*x^4 +66140687*x^5 +14462017*x^6 +624055*x^7 +1430*x^8) / (x-1)^9.
%F A194721 a(0) = 0, a(n) = 1 +(16 +(119 +(544 +(1700 +(3808 +(6188 +(7072 +4862 * (n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1) for n>0.
%e A194721 a(1) = 1: a^18 (with 1-ary alphabet {a}).
%p A194721 a:= n-> `if`(n=0, 0, (x-> 1+(16+(119+(544+(1700+(3808+(6188+(7072+4862
%p A194721                           *x)*x)*x)*x)*x)*x)*x)*x)(n-1)):
%p A194721 seq(a(n), n=0..30);
%Y A194721 Row n=9 of A183134.
%K A194721 nonn
%O A194721 0,3
%A A194721 _Alois P. Heinz_, Sep 02 2011