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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.

%I A157832 #12 Jan 26 2020 20:54:45
%S A157832 1,1,-1,5,-6,1,125,-155,31,-1,15625,-19500,4030,-156,1,9765625,
%T A157832 -12203125,2538250,-101530,781,-1,30517578125,-38144531250,7944234375,
%U A157832 -319819500,2542155,-3906,1,476837158203125,-596038818359375
%N 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.
%C A157832 Except for n=0, the row sums are zero.
%C A157832 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
%e A157832 Triangle begins
%e A157832   1;
%e A157832   1, -1;
%e A157832   5, -6, 1;
%e A157832   125, -155, 31, -1;
%e A157832   15625, -19500, 4030, -156, 1;
%e A157832   9765625, -12203125, 2538250, -101530, 781, -1;
%e A157832   30517578125, -38144531250, 7944234375, -319819500, 2542155, -3906, 1;
%e A157832   476837158203125, -596038818359375, 124166806640625, -5005123921875, 40040991375, -63573405, 19531, -1;
%p A157832 A157832 := proc(n,k)
%p A157832         product( 5^(i-1)-x,i=1..n) ;
%p A157832         coeftayl(%,x=0,k) ;
%p A157832 end proc: # _R. J. Mathar_, Oct 15 2013
%t A157832 p[x_, n_] = If[n == 0, 1, Product[q^(i - 1) - x, {i, 1, n}]];
%t A157832 q = 5;
%t A157832 Table[CoefficientList[p[x, n], x], {n, 0, 10}];
%t A157832 Flatten[%]
%Y A157832 Cf. A135950, A157783, A109345 (first column), A003463 (first subdiagonal).
%K A157832 sign,tabl
%O A157832 0,4
%A A157832 _Roger L. Bagula_, Mar 07 2009