cp's OEIS Frontend

A114159 Triangle, read by rows, equal to the matrix inverse of R=A113389.

%I A114159 #9 Jan 21 2025 06:31:10
%S A114159 1,-3,1,3,-6,1,35,-12,-9,1,396,-29,-45,-12,1,6237,582,-462,-96,-15,1,
%T A114159 131613,30684,-6408,-1534,-165,-18,1,3518993,1300810,-96705,-34020,
%U A114159 -3515,-252,-21,1,114244366,59124226,-764835,-944334,-102180,-6675,-357,-24,1
%N A114159 Triangle, read by rows, equal to the matrix inverse of R=A113389.
%e A114159 Triangle R^-1 begins:
%e A114159   1;
%e A114159   -3,1;
%e A114159   3,-6,1;
%e A114159   35,-12,-9,1;
%e A114159   396,-29,-45,-12,1;
%e A114159   6237,582,-462,-96,-15,1;
%e A114159   131613,30684,-6408,-1534,-165,-18,1;
%e A114159   3518993,1300810,-96705,-34020,-3515,-252,-21,1;
%e A114159   ...
%e A114159 Triangle R^-2 begins:
%e A114159   1;
%e A114159   -6,1;
%e A114159   24,-12,1;
%e A114159   79,30,-18,1;
%e A114159   324,356,18,-24,1;
%e A114159   42,5523,615,-12,-30,1;
%e A114159   -79346,112533,16731,640,-60,-36,1;
%e A114159   ...
%o A114159 (PARI) {T(n,k)=local(P,Q,R,W);P=Mat(1);for(m=2,n+1,W=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,W[i,j]=1,if(j==1, W[i,1]=1,W[i,j]=(P^(3*j-2))[i-j+1,1]));));P=W); R=matrix(#P,#P,r,c,if(r>=c,(P^(3*c))[r-c+1,1])); (R^-1)[n+1,k+1]}
%Y A114159 Cf. A113370 (P), A113381 (Q), A113389 (R); A114150 (R^2*Q^-1=Q^3*P^-2), A114151 (R^-2*Q^3=Q^-1*P^2), A114152 (R^3*P^-1), A114153 (R^-1*P^3), A114154 (R^3*Q^-2), A114155 (Q^-2*P^3); A114156 (P^-1), A114158 (Q^-1).
%K A114159 sign,tabl
%O A114159 0,2
%A A114159 _Paul D. Hanna_, Nov 15 2005