A107719 Matrix cube-root of triangle A107717.

1, 1, 1, 5, 2, 1, 43, 13, 3, 1, 509, 131, 25, 4, 1, 7579, 1741, 303, 41, 5, 1, 135341, 28451, 4681, 587, 61, 6, 1, 2813851, 549757, 87039, 10449, 1011, 85, 7, 1, 66733853, 12247211, 1885177, 220023, 20445, 1603, 113, 8, 1, 1778159275, 308953453

Offset: 0

Author

Paul D. Hanna, May 30 2005

Keywords

• nonn
• tabl

Comments

Column 0 is A107720. Column 1 is A107721. Matrix inverse is A107727.

Examples

			Triangle begins:
1;
1,1;
5,2,1;
43,13,3,1;
509,131,25,4,1;
7579,1741,303,41,5,1;
135341,28451,4681,587,61,6,1;
2813851,549757,87039,10449,1011,85,7,1; ...
		

Crossrefs

Cf. A107717, A107720, A107721, A107727.

Programs

PARI

T(n,k)=local(E,L,M=matrix(n+1,n+1,m,j,if(m>=j,if(m==j,1,if(m==j+1,-3*j, -polcoeff(1-(1+sum(c=1,m-j,prod(i=0,c-1,3*i+1)*x^c)+x*O(x^(m-j)))^-1,m-j);))))^-1); L=matrix(#M,#M,r,c,if(r>=c,sum(i=1,#M,(-1)^(i-1)*(M-M^0)^i/i)[r,c])); E=matrix(#L,#L,r,c,if(r>=c,sum(i=0,#L,L^i/3^i/i!)[r,c])); if(n