OFFSET
0,2
LINKS
Geoffrey Critzer, Combinatorics of Vector Spaces over Finite Fields, Master's thesis, Emporia State University, 2018.
FORMULA
T(n,k)/A005329(n) is the coefficient of y^k*x^n in eq(x)^2/(1 - y (eq(x) - 1)) where eq(x) is the q-exponential function.
EXAMPLE
Triangle begins:
1;
2, 1;
5, 7, 3;
16, 50, 56, 21;
67, 446, 1010, 945, 315;
374, 5395, 22692, 40455, 32550, 9765;
...
MATHEMATICA
nn = 10; eq[z_] :=Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}]; Grid[Map[Select[#, # > 0 &] &,
Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0,
nn}] CoefficientList[Series[ eq[z]^2/(1 - u (eq[z] - 1)) /. q -> 2, {z, 0, nn}], {z, u}]]]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Oct 17 2017
STATUS
approved