OFFSET
0,3
COMMENTS
Triangle T = A173210 satisfies: row n of T^n = row n of (I+D)^(n^2) where D is the lower diagonal matrix: D(n+1,n)=n+1.
PROG
(PARI) {a(n)=local(M=Mat(1), N, L, C=matrix(n+1, n+1, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n, N=M; M=matrix(#N+1, #N+1, r, c, if(r>=c, if(r<=#N, (N^(#N))[r, c], (C^((#M)^2))[r, c]))); L=sum(i=1, #M, -(M^0-M)^i/i); M=sum(i=0, #M, (L/#N)^i/i!); ); M[n+1, 1]}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2010
STATUS
approved