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 A173008 Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial Product_{i=1..n} (x+4^i) in row n, column 0<=k<=n. 1

%I

%S 1,4,1,64,20,1,4096,1344,84,1,1048576,348160,22848,340,1,1073741824,

%T 357564416,23744512,371008,1364,1,4398046511104,1465657589760,

%U 97615085568,1543393280,5957952,5460,1,72057594037927936

%N Triangle T(n,k) read by rows: coefficient [x^k] of the polynomial Product_{i=1..n} (x+4^i) in row n, column 0<=k<=n.

%C Row sums are 1, 5, 85, 5525, 1419925, 1455423125, 5962868543125, 97701601079103125, 6403069829921181503125, ... (partial products of A092896).

%C Triangle T(n,k), read by rows, given by [4,12,64,240,1024,4032,16384,...] DELTA [1,0,4,0,16,0,64,0,256,0,1024,0,...] where DELTA is the operator defined in A084938. - _Philippe Deléham_, Oct 01 2011

%H Robert Israel, <a href="/A173008/b173008.txt">Table of n, a(n) for n = 0..1430</a>

%F T(n,k) = 4^n*T(n-1,k) + T(n-1,k-1) with T(0,0)=1. - _Philippe Deléham_, Oct 01 2011

%e 1,

%e 4, 1,

%e 64, 20, 1,

%e 4096, 1344, 84, 1,

%e 1048576, 348160, 22848, 340, 1,

%e 1073741824, 357564416, 23744512, 371008, 1364, 1,

%e 4398046511104, 1465657589760, 97615085568, 1543393280, 5957952, 5460, 1,

%p P:= 1: A:= 1:

%p for n from 1 to 12 do

%p P:= expand(P*(x+4^n));

%p A:= A, seq(coeff(P,x,j),j=0..n)

%p od:

%p A; # _Robert Israel_, Aug 12 2015

%t Clear[p, x, n, q]

%t p[x_, n_, q_] = If[n == 0, 1, Product[x + q^i, {i, 1, n}]];

%t Table[Table[CoefficientList[p[x, n, q], x], {n, 0, 10}], {q, 2, 10}];

%t Table[Flatten[Table[CoefficientList[p[x, n, q], x], {n, 0, 10}]], {q, 2, 10}]

%Y Cf. A108084.

%K nonn,tabl,easy

%O 0,2

%A _Roger L. Bagula_, Feb 07 2010

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Last modified September 22 10:15 EDT 2020. Contains 337289 sequences. (Running on oeis4.)