cp's OEIS Frontend

A121439 Matrix inverse of triangle A121334, where A121334(n,k) = C( n*(n+1)/2 + n-k, n-k) for n>=k>=0.

%I A121439 #3 Mar 30 2012 18:36:58
%S A121439 1,-2,1,-2,-4,1,-14,0,-7,1,-143,-22,11,-11,1,-1928,-260,-40,40,-16,1,
%T A121439 -32219,-3894,-385,-121,99,-22,1,-640784,-70644,-6496,-406,-406,203,
%U A121439 -29,1,-14753528,-1502940,-128723,-9583,259,-1184,370,-37,1,-385500056,-36631962,-2947266,-205620,-14076,3657,-2967,621
%N A121439 Matrix inverse of triangle A121334, where A121334(n,k) = C( n*(n+1)/2 + n-k, n-k) for n>=k>=0.
%C A121439 A triangle having similar properties and complementary construction is the dual triangle A121435.
%F A121439 T(n,k) = [A121412^(-n*(n+1)/2 - 1)](n,k) for n>=k>=0; i.e., row n of A121334^-1 equals row n of matrix power A121412^(-n*(n+1)/2 - 1).
%e A121439 Triangle, A121334^-1, begins:
%e A121439 1;
%e A121439 -2, 1;
%e A121439 -2, -4, 1;
%e A121439 -14, 0, -7, 1;
%e A121439 -143, -22, 11, -11, 1;
%e A121439 -1928, -260, -40, 40, -16, 1;
%e A121439 -32219, -3894, -385, -121, 99, -22, 1;
%e A121439 -640784, -70644, -6496, -406, -406, 203, -29, 1;
%e A121439 -14753528, -1502940, -128723, -9583, 259, -1184, 370, -37, 1; ...
%e A121439 Triangle A121412 begins:
%e A121439 1;
%e A121439 1, 1;
%e A121439 3, 1, 1;
%e A121439 18, 4, 1, 1;
%e A121439 170, 30, 5, 1, 1; ...
%e A121439 Row 3 of A121334^-1 equals row 3 of A121412^(-7), which begins:
%e A121439 1;
%e A121439 -7, 1;
%e A121439 7, -7, 1;
%e A121439 -14, 0, -7, 1; ...
%e A121439 Row 4 of A121334^-1 equals row 4 of A121412^(-11), which begins:
%e A121439 1;
%e A121439 -11, 1;
%e A121439 33, -11, 1;
%e A121439 -22, 22, -11, 1;
%e A121439 -143, -22, 11, -11, 1;...
%o A121439 (PARI) /* Matrix Inverse of A121334 */ {T(n,k)=local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(r*(r-1)/2+r-c,r-c)))); return((M^-1)[n+1,k+1])}
%Y A121439 Cf. A121334 (matrix inverse); A121412; variants: A121438, A121440, A121441; A121435 (dual).
%K A121439 sign,tabl
%O A121439 0,2
%A A121439 _Paul D. Hanna_, Aug 29 2006