OFFSET
0,6
COMMENTS
Row sums are:
{1, 2, 4, 12, 57, 349, 5360, 146786, 4008315, 1023152227, 210533527258,...}.
The Cyclotomic binomials turn out rational.
FORMULA
t(n,m)=If[m == 0, n!, Product[Cyclotomic[k, m + 1], {k, 1, n}]]; out_(n,m)=antidiagonal(t(n,m))
EXAMPLE
{1},
{1, 1},
{1, 1, 2},
{1, 2, 3, 6},
{1, 3, 8, 21, 24},
{1, 4, 15, 104, 105, 120},
{1, 5, 24, 315, 1040, 3255, 720},
{1, 6, 35, 744, 5355, 125840, 9765, 5040},
{1, 7, 48, 1505, 19344, 1826055, 880880, 1240155, 40320},
{1, 8, 63, 2736, 55685, 15107664, 23738715, 962801840, 21082635, 362880},
{1, 9, 80, 4599, 136800, 86590175, 317260944, 129637122615, 78949750880, 1539032355, 3628800}
MATHEMATICA
Clear[t, n, m, i, k, a, b];
t[n_, m_] = If[m == 0, n!, Product[Cyclotomic[k, m + 1], {k, 1, n}]];
a = Table[Table[t[n, m], {n, 0, 10}], {m, 0, 10}];
b = Table[Table[a[[m, n - m + 1]], {m, n, 1, -1}], {n, 1, Length[a]}];
Flatten[%]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Feb 10 2009
STATUS
approved