A123187 - OEIS

%I #17 Jul 24 2015 18:57:40

%S 1,1,13,1,26,169,1,39,507,2197,1,52,1014,8788,28561,1,65,1690,21970,

%T 142805,371293,1,78,2535,43940,428415,2227758,4826809,1,91,3549,76895,

%U 999635,7797153,33787663,62748517,1,104,4732,123032,1999270,20792408

%N Triangle of coefficients in expansion of (1+13x)^n.

%C T(n,k) equals the number of n-length words on {0,1,...,13} having n-k zeros. - _Milan Janjic_, Jul 24 2015

%F p(k, x) = (13*x + 1)*p(k - 1, x).

%F T(n,k) = 13^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k)*C(n,i)*12^(n-i). Row sums are 14^n = A001023. G.f.: 1 / [1 - x(1+13y)]. - _Mircea Merca_, Apr 28 2012

%e 1

%e 1, 13

%e 1, 26, 169

%e 1, 39, 507, 2197

%e 1, 52, 1014, 8788, 28561

%e 1, 65, 1690, 21970, 142805, 371293

%p T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+13*x)^n):

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

%t p[0, x] = 1; p[1, x] = 13*x + 1; p[k_, x_] := p[k, x] = (13*x + 1)*p[k - 1, x]; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]

%Y Cf. A013609, A013610, A013611, A013621, A038220, A038222.

%K nonn,tabl

%O 1,3

%A _Roger L. Bagula_ and _Gary W. Adamson_, Oct 03 2006