Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".
0,2
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.
Table of n, a(n) for n=0..13.
(PARI) {a(n)=local(M=Mat(1), N, L, C=matrix(n+2, n+2, r, c, if(r==c, 1, if(r==c+1, c)))); for(i=1, n+1, 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!); ); sum(k=1, n+1, M[n+1, k])}
Cf. A173210, A173211, A173212, A173213.
Sequence in context: A162955 A197314 A064448 * A110817 A189428 A110860
Adjacent sequences: A173212 A173213 A173214 * A173216 A173217 A173218
nonn
Paul D. Hanna, Feb 12 2010
approved