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A111848 Matrix log of triangle A111845, which shifts columns left and up under matrix 4th power; these terms are the result of multiplying each element in row n and column k by (n-k)!. 6

%I

%S 0,1,0,4,4,0,56,16,16,0,1728,224,64,64,0,-45696,6912,896,256,256,0,

%T -159401472,-182784,27648,3584,1024,1024,0,387212983296,-637605888,

%U -731136,110592,14336,4096,4096,0,14722642769657856,1548851933184,-2550423552,-2924544,442368,57344,16384,16384,0

%N Matrix log of triangle A111845, which shifts columns left and up under matrix 4th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.

%C Column k equals 4^k multiplied by column 0 (A111849) when ignoring zeros above the diagonal.

%F T(n, k) = 4^k*T(n-k, 0) = 4^k*A111844(n-k) for n>=k>=0.

%e Matrix log of A111845, with factorial denominators, begins:

%e 0;

%e 1/1!, 0;

%e 4/2!, 4/1!, 0;

%e 56/3!, 16/2!, 16/1!, 0;

%e 1728/4!, 224/3!, 64/2!, 64/1!, 0;

%e -45696/5!, 6912/4!, 896/3!, 256/2!, 256/1!, 0; ...

%o (PARI) L(n,k,q=4)=local(A=Mat(1),B);if(n<k || k<0,0, for(m=1,n+1,B=matrix(m,m);for(i=1,m, for(j=1,i, if(j==i,B[i,j]=1,if(j==1,B[i,j]=(A^q)[i-1,1], B[i,j]=(A^q)[i-1,j-1]));));A=B); B=sum(i=1,#A,-(A^0-A)^i/i);return((n-k)!*B[n+1,k+1]))

%Y Cf. A111845 (triangle), A111849 (column 0), A111818 (variant).

%K frac,sign,tabl

%O 0,4

%A _Paul D. Hanna_, Aug 23 2005

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Last modified May 11 15:11 EDT 2021. Contains 343791 sequences. (Running on oeis4.)