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

%I A013614 #25 May 23 2016 02:46:00
%S A013614 1,1,7,1,14,49,1,21,147,343,1,28,294,1372,2401,1,35,490,3430,12005,
%T A013614 16807,1,42,735,6860,36015,100842,117649,1,49,1029,12005,84035,352947,
%U A013614 823543,823543,1,56,1372,19208,168070,941192,3294172,6588344,5764801
%N A013614 Triangle of coefficients in expansion of (1+7x)^n.
%C A013614 T(n,k) equals the number of n-length words on {0,1,...,7} having n-k zeros. - _Milan Janjic_, Jul 24 2015
%F A013614 G.f.: 1 / (1 - x(1+7y)).
%F A013614 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
%e A013614 Triangle starts:
%e A013614 1;
%e A013614 1, 7;
%e A013614 1, 14, 49;
%e A013614 1, 21, 147, 343;
%e A013614 1, 28, 294, 1372, 2401;
%e A013614 1, 35, 490, 3430, 12005, 16807;
%e A013614 ...
%p A013614 T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+7*x)^n):
%p A013614 seq(T(n), n=0..10);  # _Alois P. Heinz_, Jul 24 2015
%t A013614 T[n_, k_] := 7^k*Binomial[n, k];
%t A013614 Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, May 23 2016 *)
%Y A013614 Cf. A000420 (right edge).
%K A013614 tabl,nonn,easy
%O A013614 0,3
%A A013614 _N. J. A. Sloane_