A194730 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.

1, 1, 19, 442, 11395, 312814, 8960878, 264735892, 8006545891, 246643289830, 7711583225338, 244082045341036, 7805301802531534, 251791585570781452, 8183989442287618300, 267755464909548758440, 8810802978165549384355, 291414010749705281701270

Offset: 0

Author

Alois P. Heinz, Sep 02 2011

Keywords

• nonn

Examples

			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}).
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..200

Crossrefs

Column k=10 of A183134.

Programs

Maple

a:= n-> `if`(n=0, 1, add(binomial (2*n, j) *(n-j) *9^j, j=0..n-1) /n):
seq(a(n), n=0..20);

Formula

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

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

a(n) ~ 9 * 36^n / (64 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Sep 07 2014