A107724 Matrix logarithm of triangle A107719, read by rows.

0, 1, 0, 4, 2, 0, 31, 10, 3, 0, 343, 88, 19, 4, 0, 4855, 1066, 199, 31, 5, 0, 83209, 16216, 2779, 382, 46, 6, 0, 1670743, 295360, 47791, 6130, 655, 64, 7, 0, 38436673, 6254824, 970849, 119182, 11929, 1036, 85, 8, 0, 996825703, 150917560, 22697647, 2703730

Offset: 0

Author

Paul D. Hanna, May 30 2005

Keywords

• nonn
• tabl

Comments

Also equals one-third of the matrix logarithm of A107717. Column 0 is A107725.

Examples

			Triangle begins:
0;
1,0;
4,2,0;
31,10,3,0;
343,88,19,4,0;
4855,1066,199,31,5,0;
83209,16216,2779,382,46,6,0;
1670743,295360,47791,6130,655,64,7,0;
38436673,6254824,970849,119182,11929,1036,85,8,0; ...
		

Crossrefs

Cf. A107717, A107719.

Programs

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,-3*j, polcoeff(1/sum(i=0,m-j,prod(r=0,i-1,3*r+1)*x^i)+O(x^m),m-j)))))^-1); L=sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i);return(if(n