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

0,4

Comments

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

Links

Table of n, a(n) for n=0..46.

Example

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; ...

Prog

(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<k || k<0, 0, E[n+1, k+1])

Crossrefs

Cf. A107717, A107720, A107721, A107727.

Sequence in context: A111544 A109281 A133289 * A229959 A174485 A334343

Adjacent sequences: A107716 A107717 A107718 * A107720 A107721 A107722

Keyword

nonn,tabl

Author

Paul D. Hanna, May 30 2005

Status

approved