A107676 Matrix cube of triangle A107671.

1, 56, 8, 7965, 513, 27, 2128064, 81856, 2368, 64, 914929500, 23846125, 469625, 7625, 125, 576689214816, 10943504136, 160767720, 1898856, 19656, 216, 500750172337212, 7250862593527, 83548607478, 776598305, 6081733, 43561, 343

Offset

0,2

Comments

Column 0 is A006690.

Links

Table of n, a(n) for n=0..27.

Formula

Matrix diagonalization method: define triangular matrix P by P(n, k) = ((n+1)^3)^(n-k)/(n-k)!, n>=k>=0 and diagonal matrix D(n, n) = n+1, then T is given by T = P^-1*D^3*P.

Example

Triangle begins:
1;
56,8;
7965,513,27;
2128064,81856,2368,64;
914929500,23846125,469625,7625,125;
576689214816,10943504136,160767720,1898856,19656,216; ...
which equals the matrix cube of triangle A107671:
1;
8,2;
513,27,3;
81856,2368,64,4;
23846125,469625,7625,125,5;
10943504136,160767720,1898856,19656,216,6; ...

Prog

(PARI) {T(n, k)=local(P=matrix(n+1, n+1, r, c, if(r>=c, (r^3)^(r-c)/(r-c)!)), D=matrix(n+1, n+1, r, c, if(r==c, r))); if(n>=k, (P^-1*D^3*P)[n+1, k+1])}

Crossrefs

Cf. A107667, A107671, A107674, A006690.

Sequence in context: A206786 A036197 A182355 * A005932 A109737 A092077

Adjacent sequences: A107673 A107674 A107675 * A107677 A107678 A107679

Keyword

nonn,tabl

Author

Paul D. Hanna, Jun 07 2005

Status

approved