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A102098 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^3](n-1,k) when n>k>=0, with T(n,n) = (n+1).

%I A102098 #5 Mar 30 2012 18:36:44
%S A102098 1,1,2,7,8,3,139,152,27,4,5711,6200,999,64,5,408354,442552,69687,3904,
%T A102098 125,6,45605881,49399320,7724835,416704,11375,216,7,7390305396,
%U A102098 8003532512,1248465852,66464960,1725875,27432,343,8,1647470410551
%N A102098 Triangular matrix, read by rows, that satisfies: T(n,k) = [T^3](n-1,k) when n>k>=0, with T(n,n) = (n+1).
%C A102098 Column 0 forms A082162. Column 1 forms A102099. Row sums form A102100. This triangle is a variant of A102086.
%F A102098 T(n, 0) = A082162(n) for n>0, with T(0, 0) = 1.
%e A102098 Rows of T begin:
%e A102098 [1],
%e A102098 [1,2],
%e A102098 [7,8,3],
%e A102098 [139,152,27,4],
%e A102098 [5711,6200,999,64,5],
%e A102098 [408354,442552,69687,3904,125,6],
%e A102098 [45605881,49399320,7724835,416704,11375,216,7],
%e A102098 [7390305396,8003532512,1248465852,66464960,1725875,27432,343,8],...
%e A102098 Matrix cube T^3 equals T excluding the main diagonal:
%e A102098 [1],
%e A102098 [7,8],
%e A102098 [139,152,27],
%e A102098 [5711,6200,999,64],
%e A102098 [408354,442552,69687,3904,125],...
%o A102098 (PARI) {T(n,k)=local(A=matrix(1,1),B);A[1,1]=1; for(m=2,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=j,if(j==1,B[i,j]=(A^3)[i-1,1], B[i,j]=(A^3)[i-1,j]));));A=B);return(A[n+1,k+1])}
%Y A102098 Cf. A082162, A102099, A102100, A102086.
%K A102098 nonn,tabl
%O A102098 0,3
%A A102098 _Paul D. Hanna_, Dec 29 2004