%I #5 Jun 13 2017 22:50:29

%S 1,2,1,5,6,1,19,39,10,1,113,327,105,14,1,966,3556,1315,203,18,1,10958,

%T 48659,19875,3367,333,22,1,156700,812462,357860,64750,6867,495,26,1,

%U 2727794,16136404,7547602,1435497,160005,12199,689,30,1

%N Matrix square of triangle A113340.

%C Transforms column k of triangle A113340 into column k+1 of A113340. Also transforms column k of triangle A113350 into column k+1 of A113350.

%e Matrix square A113340^2 starts:

%e 1;

%e 2,1;

%e 5,6,1;

%e 19,39,10,1;

%e 113,327,105,14,1;

%e 966,3556,1315,203,18,1;

%e 10958,48659,19875,3367,333,22,1;

%e 156700,812462,357860,64750,6867,495,26,1;

%e 2727794,16136404,7547602,1435497,160005,12199,689,30,1; ...

%o (PARI) T(n,k)=local(A,B);A=matrix(1,1);A[1,1]=1;for(m=2,n+1,B=matrix(m,m); for(i=1,m, for(j=1,i,if(i<3 || j==i || j>m-1,B[i,j]=1,if(j==1, B[i,1]=1,B[i,j]=(A^(2*j-1))[i-j+1,1]));));A=B);(A^2)[n+1,k+1]

%Y Cf. A113340, A113346 (column 0), A113347 (column 1), A113348 (column 2), A113349 (column 3); A113350.

%K nonn,tabl

%O 0,2

%A _Paul D. Hanna_, Nov 08 2005