A013619 Triangle of coefficients in expansion of (1+12x)^n.

1, 1, 12, 1, 24, 144, 1, 36, 432, 1728, 1, 48, 864, 6912, 20736, 1, 60, 1440, 17280, 103680, 248832, 1, 72, 2160, 34560, 311040, 1492992, 2985984, 1, 84, 3024, 60480, 725760, 5225472, 20901888, 35831808, 1, 96, 4032, 96768, 1451520, 13934592, 83607552, 286654464, 429981696

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

Examples

			1;
1, 12;
1, 24, 144;
1, 36, 432, 1728;
1, 48, 864, 6912, 20736;
1, 60, 1440, 17280, 103680, 248832;
1, 72, 2160, 34560, 311040, 1492992, 2985984;
1, 84, 3024, 60480, 725760, 5225472, 20901888, 35831808;
		

Programs

Maple

T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+12*x)^n):
seq(T(n), n=0..10);  # Alois P. Heinz, Jul 24 2015

Mathematica

Flatten[Table[CoefficientList[(1+12x)^n,x],{n,0,10}]] (* Harvey P. Dale, Oct 18 2015 *)

Formula

G.f.: 1 / (1 - x(1+12y)).

T(n,k) = 12^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*11^(n-i). Row sums are 13^n = A001022. - Mircea Merca, Apr 28 2012