A013619 - OEIS

%I #25 Oct 18 2015 12:51:38

%S 1,1,12,1,24,144,1,36,432,1728,1,48,864,6912,20736,1,60,1440,17280,

%T 103680,248832,1,72,2160,34560,311040,1492992,2985984,1,84,3024,60480,

%U 725760,5225472,20901888,35831808,1,96,4032,96768,1451520,13934592,83607552,286654464,429981696

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

%C T(n,k) equals the number of n-length words on {0,1,...,12} having n-k zeros. - _Milan Janjic_, Jul 24 2015

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

%F 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

%e 1;

%e 1, 12;

%e 1, 24, 144;

%e 1, 36, 432, 1728;

%e 1, 48, 864, 6912, 20736;

%e 1, 60, 1440, 17280, 103680, 248832;

%e 1, 72, 2160, 34560, 311040, 1492992, 2985984;

%e 1, 84, 3024, 60480, 725760, 5225472, 20901888, 35831808;

%p T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+12*x)^n):

%p seq(T(n), n=0..10);  # _Alois P. Heinz_, Jul 24 2015

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

%K tabl,nonn,easy

%O 0,3

%A _N. J. A. Sloane_