A013614 Triangle of coefficients in expansion of (1+7x)^n.

1, 1, 7, 1, 14, 49, 1, 21, 147, 343, 1, 28, 294, 1372, 2401, 1, 35, 490, 3430, 12005, 16807, 1, 42, 735, 6860, 36015, 100842, 117649, 1, 49, 1029, 12005, 84035, 352947, 823543, 823543, 1, 56, 1372, 19208, 168070, 941192, 3294172, 6588344, 5764801

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

Examples

			Triangle starts:
1;
1, 7;
1, 14, 49;
1, 21, 147, 343;
1, 28, 294, 1372, 2401;
1, 35, 490, 3430, 12005, 16807;
...
		

Crossrefs

Cf. A000420 (right edge).

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+7*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jul 24 2015

Mathematica

T[n_, k_] := 7^k*Binomial[n, k];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, May 23 2016 *)

Formula

G.f.: 1 / (1 - x(1+7y)).

T(n,k) = 7^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*6^(n-i). Row sums are 8^n = A001018. - Mircea Merca, Apr 28 2012