cp's OEIS Frontend

A111828 Matrix log of triangle A111825, which shifts columns left and up under matrix 6th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.

%I A111828 #10 Jun 13 2017 22:36:49
%S A111828 0,1,0,-4,6,0,42,-24,36,0,7296,252,-144,216,0,-7931976,43776,1512,
%T A111828 -864,1296,0,-45557382240,-47591856,262656,9072,-5184,7776,0,
%U A111828 3064554175021200,-273344293440,-285551136,1575936,54432,-31104,46656,0,801993619807364206080
%N A111828 Matrix log of triangle A111825, which shifts columns left and up under matrix 6th power; these terms are the result of multiplying each element in row n and column k by (n-k)!.
%C A111828 Column k equals 6^k multiplied by column 0 (A111829) when ignoring zeros above the diagonal.
%F A111828 T(n, k) = 6^k*T(n-k, 0) = A111829(n-k) for n>=k>=0.
%e A111828 Matrix log of A111825, with factorial denominators, begins:
%e A111828 0;
%e A111828 1/1!, 0;
%e A111828 -4/2!, 6/1!, 0;
%e A111828 42/3!, -24/2!, 36/1!, 0;
%e A111828 7296/4!, 252/3!, -144/2!, 216/1!, 0;
%e A111828 -7931976/5!, 43776/4!, 1512/3!, -864/2!, 1296/1!, 0; ...
%o A111828 (PARI) T(n,k,q=6)=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 || j==1,B[i,j]=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 A111828 Cf. A111825, A111829 (column 0); log matrices: A110504 (q=-1), A111813 (q=2), A111815 (q=3), A111818 (q=4), A111823 (q=5), A111833 (q=7), A111838 (q=8).
%K A111828 frac,sign,tabl
%O A111828 0,4
%A A111828 _Gottfried Helms_ and _Paul D. Hanna_, Aug 22 2005