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Number of 10-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.
4

%I #10 Jul 13 2015 19:04:28

%S 1,1,19,442,11395,312814,8960878,264735892,8006545891,246643289830,

%T 7711583225338,244082045341036,7805301802531534,251791585570781452,

%U 8183989442287618300,267755464909548758440,8810802978165549384355,291414010749705281701270

%N Number of 10-ary words either empty or beginning with the first character of the alphabet, that can be built by inserting n doublets into the initially empty word.

%H Alois P. Heinz, <a href="/A194730/b194730.txt">Table of n, a(n) for n = 0..200</a>

%F G.f.: 9/10 + 9/(5*(8+10*sqrt(1-36*x))).

%F a(0) = 1, a(n) = 1/n * Sum_{j=0..n-1} C(2*n,j)*(n-j)*9^j for n>0.

%F a(n) ~ 9 * 36^n / (64 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Sep 07 2014

%e a(2) = 19: aaaa, aabb, aacc, aadd, aaee, aaff, aagg, aahh, aaii, aajj, abba, acca, adda, aeea, affa, agga, ahha, aiia, ajja (with 10-ary alphabet {a,b,c,d,e,f,g,h,i,j}).

%p a:= n-> `if`(n=0, 1, add(binomial (2*n, j) *(n-j) *9^j, j=0..n-1) /n):

%p seq(a(n), n=0..20);

%Y Column k=10 of A183134.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Sep 02 2011