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.

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

Offset: 0

Author

Roger L. Bagula, Mar 07 2009

Keywords

• sign
• tabl

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

Examples

			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;
		

Crossrefs

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

Programs

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[%]