This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A105623 #5 Jun 13 2017 01:36:26 %S A105623 1,1,1,4,2,1,26,10,3,1,226,74,19,4,1,2426,706,167,31,5,1,30826,8162, %T A105623 1831,320,46,6,1,451586,110410,23843,4021,548,64,7,1,7489426,1708394, %U A105623 358339,59024,7801,866,85,8,1,138722426,29752066,6097607,987763,127985 %N A105623 Matrix square-root of triangle A105615. %C A105623 Column 0 equals A105616 (=column 1 of A105615) shift 1 place right. Column 1 is A000698 (related to double factorials) offset 1. %e A105623 Triangle begins: %e A105623 1; %e A105623 1,1; %e A105623 4,2,1; %e A105623 26,10,3,1; %e A105623 226,74,19,4,1; %e A105623 2426,706,167,31,5,1; %e A105623 30826,8162,1831,320,46,6,1; %e A105623 451586,110410,23843,4021,548,64,7,1; %e A105623 7489426,1708394,358339,59024,7801,866,85,8,1; %e A105623 138722426,29752066,6097607,987763,127985,13801,1289,109,9,1; ... %o A105623 (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)))))^-1); 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 A105623 Cf. A105615, A105616 (column 0), A000698 (column 1), A105620 (matrix inverse). %K A105623 nonn,tabl %O A105623 0,4 %A A105623 _Paul D. Hanna_, Apr 16 2005