A302595 - OEIS

%I #16 May 07 2018 03:52:53

%S 1,2,1,5,6,1,16,35,14,1,67,240,175,30,1,374,2077,2480,775,62,1,2825,

%T 23562,43617,22320,3255,126,1,29212,358775,997458,791337,188976,13335,

%U 254,1,417199,7449060,30495875,36335970,13452729,1554480,53975,510,1,8283458,213188689,1268823220,2226198875,1237845378,221753049,12608560,217175,1022,1,229755605,8473977534,72697342949,185429450580,151826763275,40848897474,3600847129,101563440,871255,2046,1

%N Triangle read by rows: T(n,k) is the number of ways to choose a k-dimensional subspace U of an n-dimensional vector space over GL(2) and then choose a subspace of U.

%F T(n,k)/A005329(n) is the coefficient of y^k*x^n in (eq(x))^2*eq(y*x) where eq(x) is the q-exponential function.

%e      1;

%e      2,     1;

%e      5,     6,     1;

%e     16,    35,    14,     1;

%e     67,   240,   175,    30,     1;

%e    374,  2077,  2480,   775,    62,     1;

%e   2825, 23562, 43617, 22320,  3255,   126,     1;

%t nn = 6; qq := 2; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}]; Map[Select[#, # > 0 &] &, Table[FunctionExpand[QFactorial[n, q]] /. q -> qq, {n, 0, nn}] CoefficientList[Series[eq[z]^2 eq[u z] /. q -> qq, {z, 0, nn}], {z, u}]] // Grid

%K nonn,tabl

%O 0,2

%A _Geoffrey Critzer_, Apr 10 2018