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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
1, 4, 1, 64, 20, 1, 4096, 1344, 84, 1, 1048576, 348160, 22848, 340, 1, 1073741824, 357564416, 23744512, 371008, 1364, 1, 4398046511104, 1465657589760, 97615085568, 1543393280, 5957952, 5460, 1, 72057594037927936 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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

LINKS

Robert Israel, Table of n, a(n) for n = 0..1430

FORMULA

T(n,k) = 4^n*T(n-1,k) + T(n-1,k-1) with T(0,0)=1. - Philippe Deléham, Oct 01 2011

EXAMPLE

1,

4, 1,

64, 20, 1,

4096, 1344, 84, 1,

1048576, 348160, 22848, 340, 1,

1073741824, 357564416, 23744512, 371008, 1364, 1,

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

MAPLE

P:= 1: A:= 1:

for n from 1 to 12 do

  P:= expand(P*(x+4^n));

  A:= A, seq(coeff(P, x, j), j=0..n)

od:

A; # Robert Israel, Aug 12 2015

MATHEMATICA

Clear[p, x, n, q]

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

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

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

CROSSREFS

Cf. A108084.

Sequence in context: A113112 A278578 A069740 * A298828 A114917 A100864

Adjacent sequences:  A173005 A173006 A173007 * A173009 A173010 A173011

KEYWORD

nonn,tabl,easy

AUTHOR

Roger L. Bagula, Feb 07 2010

STATUS

approved

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Last modified May 24 17:09 EDT 2019. Contains 323533 sequences. (Running on oeis4.)