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%I #19 Jul 17 2017 02:37:13
%S 1,3,12,66,513,5769,95706,2379348,89759799,5188919427,463209471288,
%T 64236626341974,13903296824817117,4713694025825766861,
%U 2510421030027019810854,2104931848782489253483752,2783505220978001187684672531,5813031971452642599096778614183
%N Number of ways to choose a subspace U of GF(2)^n and then choose a subspace of U.
%C A q-analog (q=2) of A000244.
%F a(n) = Sum_{k=0..n} A022166(n,k)*A006116(k).
%F a(n)/[n]_q! is the coefficient of x^n in the expansion of exp_q(x)^3 when q -> 2 and where exp_q(x) is the q-exponential function and [n]_q! is the q-factorial of n.
%t nn = 20; eq[z_] := Sum[z^n/FunctionExpand[QFactorial[n, q]], {n, 0, nn}];
%t Table[FunctionExpand[QFactorial[n, q]] /. q -> 2, {n, 0, nn}] CoefficientList[ Series[eq[z]^3 /. q -> 2, {z, 0, nn}], z]
%Y Cf. A000244, A182176, A289537, A289538, A289541, A289542.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Jul 12 2017
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