A013616 Triangle of coefficients in expansion of (1+9x)^n.

1, 1, 9, 1, 18, 81, 1, 27, 243, 729, 1, 36, 486, 2916, 6561, 1, 45, 810, 7290, 32805, 59049, 1, 54, 1215, 14580, 98415, 354294, 531441, 1, 63, 1701, 25515, 229635, 1240029, 3720087, 4782969, 1, 72, 2268, 40824, 459270, 3306744, 14880348, 38263752, 43046721

Offset: 0

Author

N. J. A. Sloane

Keywords

• tabl
• nonn
• easy

Comments

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

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+9*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jun 10 2014

Formula

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

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