cp's OEIS Frontend

A107726 Matrix inverse of triangle A107717, read by rows.

%I A107726 #5 Jun 13 2017 02:01:17
%S A107726 1,-3,1,-3,-6,1,-21,-3,-9,1,-219,-21,-3,-12,1,-2973,-219,-21,-3,-15,1,
%T A107726 -49323,-2973,-219,-21,-3,-18,1,-964173,-49323,-2973,-219,-21,-3,-21,
%U A107726 1,-21680571,-964173,-49323,-2973,-219,-21,-3,-24,1,-551173053,-21680571,-964173,-49323,-2973,-219,-21,-3,-27,1
%N A107726 Matrix inverse of triangle A107717, read by rows.
%C A107726 Except for initial terms, each column is the same and equals negative A107716 (inverse INVERT of triple factorials).
%e A107726 Triangle begins:
%e A107726 1;
%e A107726 -3,1;
%e A107726 -3,-6,1;
%e A107726 -21,-3,-9,1;
%e A107726 -219,-21,-3,-12,1;
%e A107726 -2973,-219,-21,-3,-15,1;
%e A107726 -49323,-2973,-219,-21,-3,-18,1;
%e A107726 -964173,-49323,-2973,-219,-21,-3,-21,1; ...
%e A107726 Matrix inverse is A107717:
%e A107726 1;
%e A107726 3,1;
%e A107726 21,6,1;
%e A107726 219,57,9,1;
%e A107726 2973,723,111,12,1;
%e A107726 49323,11361,1713,183,15,1; ...
%o A107726 (PARI) T(n,k)=if(n<k || k<0,0,matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, polcoeff(1/sum(i=0,m-j,prod(r=0,i-1,3*r+1)*x^i)+O(x^m),m-j)))))[n+1,k+1])
%Y A107726 Cf. A107716, A107717.
%K A107726 sign,tabl
%O A107726 0,2
%A A107726 _Paul D. Hanna_, May 30 2005