A105623 Matrix square-root of triangle A105615.

1, 1, 1, 4, 2, 1, 26, 10, 3, 1, 226, 74, 19, 4, 1, 2426, 706, 167, 31, 5, 1, 30826, 8162, 1831, 320, 46, 6, 1, 451586, 110410, 23843, 4021, 548, 64, 7, 1, 7489426, 1708394, 358339, 59024, 7801, 866, 85, 8, 1, 138722426, 29752066, 6097607, 987763, 127985

Offset: 0

Author

Paul D. Hanna, Apr 16 2005

Keywords

• nonn
• tabl

Comments

Column 0 equals A105616 (=column 1 of A105615) shift 1 place right. Column 1 is A000698 (related to double factorials) offset 1.

Examples

			Triangle begins:
1;
1,1;
4,2,1;
26,10,3,1;
226,74,19,4,1;
2426,706,167,31,5,1;
30826,8162,1831,320,46,6,1;
451586,110410,23843,4021,548,64,7,1;
7489426,1708394,358339,59024,7801,866,85,8,1;
138722426,29752066,6097607,987763,127985,13801,1289,109,9,1; ...
		

Crossrefs

Cf. A105615, A105616 (column 0), A000698 (column 1), A105620 (matrix inverse).

Programs

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