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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 June 8 13:50 EDT 2023. Contains 363165 sequences. (Running on oeis4.)