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Triangle of coefficients in expansion of (1+5x)^n.
5

%I #23 Feb 13 2016 10:42:34

%S 1,1,5,1,10,25,1,15,75,125,1,20,150,500,625,1,25,250,1250,3125,3125,1,

%T 30,375,2500,9375,18750,15625,1,35,525,4375,21875,65625,109375,78125,

%U 1,40,700,7000,43750,175000,437500,625000,390625,1,45,900,10500,78750,393750,1312500,2812500,3515625,1953125

%N Triangle of coefficients in expansion of (1+5x)^n.

%C Mirror image of A038243. - _Zerinvary Lajos_, Nov 25 2007

%C T(n,k) equals the number of n-length words on {0,1,...,5} having n-k zeros. - _Milan Janjic_, Jul 24 2015

%H Alois P. Heinz, <a href="/A013612/b013612.txt">Rows n = 0..140, flattened</a>

%F G.f.: 1 / [1 - x(1+5y)].

%F T(n,k) = 5^k*C(n,k) = Sum_{i=n-k..n} C(i,n-k) *C(n,i) *4^(n-i). Row sums are 6^n = A000400(n). - _Mircea Merca_, Apr 28 2012

%p T:= n-> (p-> seq(coeff(p, x, k), k=0..n))((1+5*x)^n):

%p seq(T(n), n=0..10); # _Alois P. Heinz_, Jun 10 2014

%t row[n_] := CoefficientList[(1 + 5x)^n, x]; Table[row[n], {n, 0, 9}] // Flatten (* _Jean-François Alcover_, Feb 13 2016 *)

%K tabl,nonn,easy

%O 0,3

%A _N. J. A. Sloane_.