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%I #6 Jun 13 2017 01:36:44
%S 1,3,1,18,6,1,150,48,9,1,1566,480,93,12,1,19494,5736,1125,153,15,1,
%T 280998,79584,15681,2190,228,18,1,4598910,1256808,247929,35181,3780,
%U 318,21,1,84237246,22262640,4389213,629424,68961,6000,423,24,1,1707637734
%N Triangular matrix T, read by rows, that satisfies T^2 = A105615^3; also equals the matrix cube of triangle A105623.
%C SHIFT_LEFT(column 0 of T) = 3*(column 2 of A105615). A105623 equals the matrix square-root of triangle A105615.
%F T(n+1, 0) = 3*A105615(n+2, 2) = 3*A105617(n) for n>=0.
%e Triangle begins:
%e 1;
%e 3,1;
%e 18,6,1;
%e 150,48,9,1;
%e 1566,480,93,12,1;
%e 19494,5736,1125,153,15,1;
%e 280998,79584,15681,2190,228,18,1;
%e 4598910,1256808,247929,35181,3780,318,21,1;
%e 84237246,22262640,4389213,629424,68961,6000,423,24,1; ...
%o (PARI) T(n,k)=local(R,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-2*j, polcoeff(1/sum(i=0,m-j,(2*i)!/i!/2^i*x^i)+O(x^m),m-j)))))^-3); R=(M+M^0)/2;for(i=1,floor(2*log(n+2)),R=(R+M*R^(-1))/2); return(if(n<k || k<0,0,R[n+1,k+1]))
%Y Cf. A105615, A105617, A105623, A105627 (column 1), A105628 (row sums).
%K nonn,tabl
%O 0,2
%A _Paul D. Hanna_, Apr 16 2005
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