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%I #12 Feb 08 2023 09:49:55
%S 1,-1,5,1,-35,90,-3,595,-6885,12005,143,-150535,6175845,-39484445,
%T 52245760,-58201,316465625,-42458934375,772604284375,-3322503800000,
%U 3547818864576,216931,-6012846875,2544269990625,-120371747505625,1294115230100000,-4145626343257056,3713894747640000
%N Triangle of signed numbers used for the computation of the column sequences of triangle A090215.
%C A090215(n+m,m)= sum(a(m,p)*((p+3)*(p+2)*(p+1)*p)^n,p=1..m)/D(m) with D(m) := A089516(m); m=1,2,..., n>=0.
%H Wolfdieter Lang, <a href="/A089515/a089515.txt">First 7 rows</a>.
%F a(n, m)= D(n)*((-1)^(n-m))*(fallfac(m+3, 4)^(n-1))/(product(fallfac(m+3, 4)-fallfac(r+3, 4), r=1..m-1)*product(fallfac(r+3, 4)-fallfac(m+3, 4), r=m+1..n)), with D(n) := A089516(n) and fallfac(n, m) := A008279(n, m) (falling factorials), 1<=m<=n else 0. (Replace in the denominator the first product by 1 if m=1 and the second one by 1 if m=n.)
%e Triangle begins:
%e 1;
%e -1, 5;
%e 1, -35, 90;
%e -3, 595,-6885, 12005;
%e ...
%e A090215(2+3,3) = 199296 = (1*(4*3*2*1)^2 - 35*(5*4*3*2)^2 + 90*(6*5*4*3)^2)/56.
%e a(3,2)= -35 = 56*(-1)*((5*4*3*2)^2)/((5*4*3*2-4*3*2*1)*(6*5*4*3-5*4*3*2)).
%K sign,easy,tabl
%O 1,3
%A _Wolfdieter Lang_, Dec 01 2003
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