A173215 - OEIS

%I #2 Mar 30 2012 18:37:21

%S 1,2,9,130,5801,549066,86723617,20271902834,6531967419105,

%T 2765255048181586,1485110148765267161,985070868793251223842,

%U 790007920377720295086409,752911901689684021069284410

%N Row sums of triangle A173210.

%C 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.

%o (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])}

%Y Cf. A173210, A173211, A173212, A173213.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 12 2010