cp's OEIS Frontend

A121441 Matrix inverse of triangle A121336, where A121336(n,k) = C( n*(n+1)/2 + n-k + 2, n-k) for n>=k>=0.

%I A121441 #3 Mar 30 2012 18:36:58
%S A121441 1,-4,1,3,-6,1,-12,9,-9,1,-117,-26,26,-13,1,-1656,-216,-69,63,-18,1,
%T A121441 -28506,-3396,-294,-212,132,-24,1,-578274,-63116,-5766,-124,-620,248,
%U A121441 -31,1,-13504179,-1365546,-116116,-8892,1170,-1612,429,-39,1,-356633784,-33696726,-2696316,-186860,-15000,6228,-3736
%N A121441 Matrix inverse of triangle A121336, where A121336(n,k) = C( n*(n+1)/2 + n-k + 2, n-k) for n>=k>=0.
%C A121441 A triangle having similar properties and complementary construction is the dual triangle A121437.
%F A121441 T(n,k) = [A121412^(-n*(n+1)/2 - 3)](n,k) for n>=k>=0; i.e., row n of A121336^-1 equals row n of matrix power A121412^(-n*(n+1)/2 - 3).
%e A121441 Triangle, A121336^-1, begins:
%e A121441 1;
%e A121441 -4, 1;
%e A121441 3, -6, 1;
%e A121441 -12, 9, -9, 1;
%e A121441 -117, -26, 26, -13, 1;
%e A121441 -1656, -216, -69, 63, -18, 1;
%e A121441 -28506, -3396, -294, -212, 132, -24, 1;
%e A121441 -578274, -63116, -5766, -124, -620, 248, -31, 1;
%e A121441 -13504179, -1365546, -116116, -8892, 1170, -1612, 429, -39, 1; ...
%e A121441 Triangle A121412 begins:
%e A121441 1;
%e A121441 1, 1;
%e A121441 3, 1, 1;
%e A121441 18, 4, 1, 1;
%e A121441 170, 30, 5, 1, 1; ...
%e A121441 Row 3 of A121336^-1 equals row 3 of A121412^(-9), which begins:
%e A121441 1;
%e A121441 -9, 1;
%e A121441 18, -9, 1;
%e A121441 -12, 9, -9, 1; ...
%e A121441 Row 4 of A121336^-1 equals row 4 of A121412^(-13), which begins:
%e A121441 1;
%e A121441 -13, 1;
%e A121441 52, -13, 1;
%e A121441 -52, 39, -13, 1;
%e A121441 -117, -26, 26, -13, 1; ...
%o A121441 (PARI) /* Matrix Inverse of A121336 */ {T(n,k)=local(M=matrix(n+1,n+1,r,c,if(r>=c,binomial(r*(r-1)/2+r-c+2,r-c)))); return((M^-1)[n+1,k+1])}
%Y A121441 Cf. A121336 (matrix inverse); A121412; variants: A121438, A121439, A121440; A121437 (dual).
%K A121441 sign,tabl
%O A121441 0,2
%A A121441 _Paul D. Hanna_, Aug 29 2006