A173221 - OEIS

%I #8 Feb 03 2023 04:53:15

%S 0,1,2,60,3528,377620,63642600,15485843814,5128034120832,

%T 2214330161840640,1207205860726123200,810202288257005858280,

%U 655934516902959161345280,630002861547863478457648320

%N Column 0 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+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!); ); L[n+1, 1]/(n+1)}

%Y Cf. A173210, A173220, A173222, A173223, A173224.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Feb 12 2010