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%I #7 Apr 11 2020 02:42:04
%S 1,3,14,114,1777,55461,3496868,444131448,113253936439,57872769803787,
%T 59203843739029706,121190268142727296926,496274148044956457612893,
%U 4064981546636275903297015089,66596592678542112197488335080432,2182170552297789390998576752287351492
%N Total number of saturated chains in the lattices L_n(2) of subspaces (ordered by inclusion) of the vector space GF(2)^n.
%C These are the chains counted in A293844 that are saturated. A chain C in poset P is saturated if there is no z in P - C such that x < z < y for some x,y in C and such that C union {z} is a chain.
%F a(n)/A005329(n) is the coefficient of x^n in eq(x)^2/(1 - x) where eq(x) is the q-exponential function.
%F a(n) ~ A299998 * 2^(n*(n+1)/2). - _Vaclav Kotesovec_, Apr 07 2020
%t nn = 15; 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]^2/(1 - z) /. q -> 2, {z, 0, nn}], z]
%Y Cf. A289545, A293844.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, Apr 05 2020
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