A329819 Triangular array, read by rows: T(n,k) = [(x*y*z)^k] (-1 + (1 + x + 1/x)*(1 + y + 1/y)*(1 + z + 1/z))^n for -n <= k <= n.

1, 1, 0, 1, 1, 6, 26, 6, 1, 1, 24, 195, 264, 195, 24, 1, 1, 60, 898, 3276, 5646, 3276, 898, 60, 1, 1, 120, 3065, 22260, 72730, 101520, 72730, 22260, 3065, 120, 1, 1, 210, 8526, 105690, 581475, 1510860, 2103740, 1510860, 581475, 105690, 8526, 210, 1

Offset

0,6

Links

Seiichi Manyama, Rows n = 0..25, flattened

Formula

T(n,k) = T(n,-k).

Example

Triangle begins:
                                 1;
                         1,      0,     1;
                  1,     6,     26,     6,     1;
           1,    24,   195,    264,   195,    24,    1;
     1,   60,   898,  3276,   5646,  3276,   898,   60,   1;
1, 120, 3065, 22260, 72730, 101520, 72730, 22260, 3065, 120, 1;

Prog

(PARI) {T(n, k) = polcoef(polcoef(polcoef((-1+(1+x+1/x)*(1+y+1/y)*(1+z+1/z))^n, k), k), k)}

Crossrefs

T(n,0) gives A328874.

Cf. A260492, A329816, A329820.

Sequence in context: A005938 A157025 A174401 * A337400 A036175 A239178

Adjacent sequences: A329816 A329817 A329818 * A329820 A329821 A329822

Keyword

nonn,tabf

Author

Seiichi Manyama, Nov 21 2019

Status

approved