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Triangle of coefficients in expansion of (1+9x)^n.
3

%I #24 Jul 24 2015 18:53:46

%S 1,1,9,1,18,81,1,27,243,729,1,36,486,2916,6561,1,45,810,7290,32805,

%T 59049,1,54,1215,14580,98415,354294,531441,1,63,1701,25515,229635,

%U 1240029,3720087,4782969,1,72,2268,40824,459270,3306744,14880348,38263752,43046721

%N Triangle of coefficients in expansion of (1+9x)^n.

%C T(n,k) equals the number of n-length words on {0,1,...,9} having n-k zeros. - _Milan Janjic_, Jul 24 2015

%F G.f.: 1 / (1 - x(1+9y)).

%F T(n,k) = 9^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*8^(n-i). Row sums are 10^n = A011557(n). - _Mircea Merca_, Apr 28 2012

%p T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+9*x)^n):

%p seq(T(n), n=0..10); # _Alois P. Heinz_, Jun 10 2014

%K tabl,nonn,easy

%O 0,3

%A _N. J. A. Sloane_