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A194722 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting ten doublets into the initially empty word.

%I A194722 #9 Jul 13 2015 19:09:50
%S A194722 0,1,92378,19319845,560198962,6507351113,44731364266,218878998733,
%T A194722 844131474530,2730108129937,7711583225338,19564269083381,
%U A194722 45486599105938,98378219490265,200201768681162,386776488742813,714420272913346,1268930908616993,2177477525153050
%N A194722 Number of n-ary words beginning with the first character of the alphabet, that can be built by inserting ten doublets into the initially empty word.
%H A194722 Alois P. Heinz, <a href="/A194722/b194722.txt">Table of n, a(n) for n = 0..1000</a>
%F A194722 G.f.: x * (1 +92368*x +18396110*x^2 +371157402*x^3 +1763669368*x^4 +2567824154*x^5 +1206169122*x^6 +163325950*x^7 +4293143*x^8 +4862*x^9) / (x-1)^10.
%F A194722 a(0) = 0, a(n) = 1 +(18 +(152 +(798 +(2907 +(7752 +(15504 +(23256 +(25194 +16796*(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) *(n-1)) * (n-1)) * (n-1) for n>0.
%e A194722 a(1) = 1: a^20 (with 1-ary alphabet {a}).
%p A194722 a:= n-> `if`(n=0, 0, (x-> 1+(18+(152+(798+(2907+(7752+(15504+(23256+
%p A194722                      (25194+16796*x)*x)*x)*x)*x)*x)*x)*x)*x)(n-1)):
%p A194722 seq(a(n), n=0..30);
%Y A194722 Row n=10 of A183134.
%K A194722 nonn
%O A194722 0,3
%A A194722 _Alois P. Heinz_, Sep 02 2011