A013617 Triangle of coefficients in expansion of (1+10x)^n.

1, 1, 10, 1, 20, 100, 1, 30, 300, 1000, 1, 40, 600, 4000, 10000, 1, 50, 1000, 10000, 50000, 100000, 1, 60, 1500, 20000, 150000, 600000, 1000000, 1, 70, 2100, 35000, 350000, 2100000, 7000000, 10000000, 1, 80, 2800, 56000, 700000, 5600000, 28000000, 80000000, 100000000

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,...,10} having n-k zeros. - Milan Janjic, Jul 24 2015

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+10*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jul 24 2015

Formula

G.f.: 1 / (1 - x(1+10y)).

T(n,k) = 10^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*9^(n-i). Row sums are 11^n = A001020. - Mircea Merca, Apr 28 2012