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A105629 Triangular matrix, read by rows, equal to the matrix logarithm of triangle A105623.

%I A105629 #5 Jun 13 2017 01:36:48
%S A105629 0,1,0,3,2,0,17,7,3,0,135,43,13,4,0,1353,361,93,21,5,0,16251,3779,883,
%T A105629 175,31,6,0,226857,47077,10277,1893,297,43,7,0,3605775,678443,140743,
%U A105629 24735,3631,467,57,8,0,64288209,11095201,2211413,376209,52961,6385,693
%N A105629 Triangular matrix, read by rows, equal to the matrix logarithm of triangle A105623.
%C A105629 Also equals (1/2) the matrix logarithm of triangle A105615, since A105623 equals the matrix square-root of triangle A105615.
%e A105629 Triangle begins:
%e A105629 0;
%e A105629 1,0;
%e A105629 3,2,0;
%e A105629 17,7,3,0;
%e A105629 135,43,13,4,0;
%e A105629 1353,361,93,21,5,0;
%e A105629 16251,3779,883,175,31,6,0;
%e A105629 226857,47077,10277,1893,297,43,7,0;
%e A105629 3605775,678443,140743,24735,3631,467,57,8,0;
%e A105629 64288209,11095201,2211413,376209,52961,6385,693,73,9,0; ...
%o A105629 (PARI) T(n,k)=local(L,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)))))^-1); L=sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i); return(if(n<k || k<0,0,L[n+1,k+1]/2))
%Y A105629 Cf. A105615, A105623, A105630 (column 0), A105631 (row sums).
%K A105629 nonn,tabl
%O A105629 0,4
%A A105629 _Paul D. Hanna_, Apr 16 2005