A157832 - OEIS

%I #12 Jan 26 2020 20:54:45

%S 1,1,-1,5,-6,1,125,-155,31,-1,15625,-19500,4030,-156,1,9765625,

%T -12203125,2538250,-101530,781,-1,30517578125,-38144531250,7944234375,

%U -319819500,2542155,-3906,1,476837158203125,-596038818359375

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

%C 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 Triangle begins

%e   1;

%e   1, -1;

%e   5, -6, 1;

%e   125, -155, 31, -1;

%e   15625, -19500, 4030, -156, 1;

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

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

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

%p A157832 := proc(n,k)

%p         product( 5^(i-1)-x,i=1..n) ;

%p         coeftayl(%,x=0,k) ;

%p end proc: # _R. J. Mathar_, Oct 15 2013

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

%t q = 5;

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

%t Flatten[%]

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

%K sign,tabl

%O 0,4

%A _Roger L. Bagula_, Mar 07 2009