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A157832 Triangle read by rows: the coefficient [x^k] of the polynomial Product_{i=1..n} (5^(i-1)-x) in row n, column k, 0 <= k <= n. 5
1, 1, -1, 5, -6, 1, 125, -155, 31, -1, 15625, -19500, 4030, -156, 1, 9765625, -12203125, 2538250, -101530, 781, -1, 30517578125, -38144531250, 7944234375, -319819500, 2542155, -3906, 1, 476837158203125, -596038818359375 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Except for n=0, the row sums are zero.

Triangle T(n,k), 0 <= k <= n, read by rows given by [1,q-1,q^2,q^3-q,q^4,q^5-q^2,q^6,q^7-q^3,q^8,...] DELTA [ -1,0,-q,0,-q^2,0,-q^3,0,-q^4,0,...] (for q=5)= [1,4,25,120,625,3100,15625,...] DELTA [ -1,0,-5,0,-25,0,-125,0,-625,0,...] where DELTA is the operator defined in A084938. - Philippe Deléham, Mar 10 2009

LINKS

Table of n, a(n) for n=0..29.

EXAMPLE

Triangle begins

  1;

  1, -1;

  5, -6, 1;

  125, -155, 31, -1;

  15625, -19500, 4030, -156, 1;

  9765625, -12203125, 2538250, -101530, 781, -1;

  30517578125, -38144531250, 7944234375, -319819500, 2542155, -3906, 1;

  476837158203125, -596038818359375, 124166806640625, -5005123921875, 40040991375, -63573405, 19531, -1;

MAPLE

A157832 := proc(n, k)

        product( 5^(i-1)-x, i=1..n) ;

        coeftayl(%, x=0, k) ;

end proc: # R. J. Mathar, Oct 15 2013

MATHEMATICA

p[x_, n_] = If[n == 0, 1, Product[q^(i - 1) - x, {i, 1, n}]];

q = 5;

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

Flatten[%]

CROSSREFS

Cf. A135950, A157783, A109345 (first column), A003463 (first subdiagonal).

Sequence in context: A293107 A113106 A171273 * A330660 A200486 A182496

Adjacent sequences:  A157829 A157830 A157831 * A157833 A157834 A157835

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Mar 07 2009

STATUS

approved

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Last modified September 25 12:47 EDT 2020. Contains 337344 sequences. (Running on oeis4.)