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%I #5 Jun 13 2017 23:23:09
%S 1,3,15,136,1998,41973,1166263,40747561,1726907675,86421647389,
%T 5002021986418,329382745551946,24351172588548270,1999205882982496161,
%U 180613538916429940159,17817366508243503227269
%N Column 0 of triangle A113378, also equals column 0 of A113389.
%F A113378 equals the matrix cube of A113370, which has the property: column k of A113370^3 = column 0 of A113389^(3*k+1) for k>=0.
%o (PARI) a(n)=local(A,B);A=Mat(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^(3*j-2))[i-j+1,1]));));A=B);(A^3)[n+1,1]
%Y Cf. A113378, A113370, A113389, A113380 (column 1).
%K nonn
%O 0,2
%A _Paul D. Hanna_, Nov 14 2005
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