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%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
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