A013615 Triangle of coefficients in expansion of (1+8x)^n.

1, 1, 8, 1, 16, 64, 1, 24, 192, 512, 1, 32, 384, 2048, 4096, 1, 40, 640, 5120, 20480, 32768, 1, 48, 960, 10240, 61440, 196608, 262144, 1, 56, 1344, 17920, 143360, 688128, 1835008, 2097152, 1, 64, 1792, 28672, 286720, 1835008, 7340032, 16777216, 16777216

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

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+8*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jul 25 2015

Formula

G.f.: 1 / [1 - x(1+8y)].

T(n,k) = 8^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*7^(n-i). Row sums are 9^n = A001019. - Mircea Merca, Apr 28 2012