A173223 - OEIS

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

%S 0,12,90,4320,418950,68045040,16408798560,5461729378560,

%T 2388307104414000,1323740028257460000,905000067758493495360,

%U 747005694270473162004480,731648558087385682524580800

%N Column 2 of triangle A173220.

%C Triangle A173220 is the matrix log of triangle T = A173210, which 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=Mat(1), C=matrix(n+4,n+4,r,c,if(r==c,1,if(r==c+1,c)))); for(i=1, n+3, 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!); ); L[n+3, 3]/(n+2)}

%Y Cf. A173220, A173221, A173222, A173224.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Feb 12 2010