OFFSET
0,5
COMMENTS
Row sums are:
{1, 2, 4, 12, 56, 348, 2768, 29092, 416952, 8282956, 229754592,...}.
FORMULA
q=2;
c(n,q)=Product[1 - q^i, {i, 1, n}];
t(n,m,q)=t(n,m,q)=1 c(n, q)/(c[m, q)*c(n - m, q))-Binomial[n, m]
EXAMPLE
{1},
{1, 1},
{1, 2, 1},
{1, 5, 5, 1},
{1, 12, 30, 12, 1},
{1, 27, 146, 146, 27, 1},
{1, 58, 637, 1376, 637, 58, 1},
{1, 121, 2647, 11777, 11777, 2647, 121, 1},
{1, 248, 10768, 97100, 200718, 97100, 10768, 248, 1},
{1, 503, 43400, 787952, 3309622, 3309622, 787952, 43400, 503, 1},
{1, 1014, 174207, 6347596, 53743778, 109221400, 53743778, 6347596, 174207, 1014, 1}
MATHEMATICA
c[n_, q_] = Product[1 - q^i, {i, 1, n}];
t[n_, m_, q_] = c[n, q]/(c[m, q]*c[n - m, q]) - Binomial[n, m] + 1;
Table[Flatten[Table[Table[t[n, m, q], {m, 0, n}], {n, 0, 10}]], {q, 2, 12}]
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Apr 17 2010
STATUS
approved