login
A173223
Column 2 of triangle A173220.
4
0, 12, 90, 4320, 418950, 68045040, 16408798560, 5461729378560, 2388307104414000, 1323740028257460000, 905000067758493495360, 747005694270473162004480, 731648558087385682524580800
OFFSET
0,2
COMMENTS
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.
PROG
(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)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2010
STATUS
approved