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%I #5 Jun 13 2017 23:40:27
%S 1,-1,1,3,-4,1,6,0,-7,1,-8,38,-21,-10,1,-501,692,-119,-60,-13,1,
%T -13623,14910,-420,-735,-117,-16,1,-409953,401802,22911,-12470,-2080,
%U -192,-19,1,-14544683,13278520,1577527,-255570,-51064,-4424,-285,-22,1
%N Triangle, read by rows, equal to the matrix inverse of P=A113370.
%e Triangle P^-1 begins:
%e 1;
%e -1,1;
%e 3,-4,1;
%e 6,0,-7,1;
%e -8,38,-21,-10,1;
%e -501,692,-119,-60,-13,1;
%e -13623,14910,-420,-735,-117,-16,1;
%e -409953,401802,22911,-12470,-2080,-192,-19,1; ...
%e Triangle P^-2 begins:
%e 1;
%e -2,1;
%e 10,-8,1;
%e -9,28,-14,1;
%e -177,160,28,-20,1;
%e -2307,1366,455,10,-26,1;
%e -38874,15982,8666,660,-26,-32,1; ...
%o (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); (P^-1)[n+1,k+1]
%Y Cf. A114157 (column 0), 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); A114158 (Q^-1), A114159 (R^-1).
%K sign,tabl
%O 0,4
%A _Paul D. Hanna_, Nov 15 2005
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