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A173224
Row sums of triangle A173220.
4
0, 1, 6, 87, 4288, 433045, 70899306, 16947087955, 5544027333440, 2372735984247009, 1284753824984593630, 857573459327085778431, 691208427837113229333984, 661423852799242010825878453
OFFSET
0,3
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+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, L[n+1, k])/(n+1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 12 2010
STATUS
approved