OFFSET
0,8
COMMENTS
Row sums are:
1, 2, 2, 242, 6842, 174442, 4575342, 120319754, 3218718386, 87130425890,
2387489480048,...
FORMULA
q=4;
t(n,m,q)=If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, -Floor[q/2], Floor[q/2]}] +
Product[Binomial[n + i, n - m + i], {i, -Floor[q/2], Floor[q/2]}]]
EXAMPLE
{1},
{1, 1},
{1, 0, 1},
{1, 120, 120, 1},
{1, 720, 5400, 720, 1},
{1, 2520, 84700, 84700, 2520, 1},
{1, 6720, 712950, 3136000, 712950, 6720, 1},
{1, 15120, 4064256, 56080500, 56080500, 4064256, 15120, 1},
{1, 30240, 17745840, 619178112, 1944810000, 619178112, 17745840, 30240, 1},
{1, 55440, 63795600, 4857209280, 38644152624, 38644152624, 4857209280, 63795600, 55440, 1},
{1, 95040, 197735175, 29523225600, 513405390960, 1301236586496, 513405390960, 29523225600, 197735175, 95040, 1}
MATHEMATICA
t[n_, m_, q_] = If[n == 0 || n == 1, 1, Product[Binomial[n + i, m + i], {i, - Floor[q/2], Floor[q/2]}] + Product[Binomial[n + i, n - m + i], { i, -Floor[q/2], Floor[q/2]}]];
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 0, 10, 2}]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Mar 09 2010
STATUS
approved