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%I #16 Jan 19 2019 03:53:30
%S 2,6,36,420,9800,452760,41835024,7691667984,2828336198688,
%T 2073619375892064,3040584296923128384,8898500292240756664896,
%U 52084270468105185237918848,608812309050346291991694422400
%N Total dimension of the homology of a free 2-step nilpotent Lie algebra of rank n.
%H J. Grassberger, A. King, P. Tirao, <a href="https://doi.org/10.1016/S0021-8693(02)00090-X">On the homology of free 2-step nilpotent Lie algebras</a>, J. Algebra 254 (2002), 213-225.
%F a(n) = 2^ceiling(n/2)*f(floor((n-1)/2))*f(floor(n/2)), where f(n)= Product_{i=1..n} (4*i)!*i!^2/((2*i)!)^3.
%F a(n) ~ K*2^(n^2/2)*n^(1/8), where K=1.3814... - _Nordine Fahssi_, Jan 17 2019
%F From _Jon E. Schoenfield_, Jan 17 2019: (Start)
%F K = 1.38143139396100192327615434710888289668811010590733/
%F 41912628937302462176044631403587011199108546012939...
%F (End)
%p f := proc(n) local i: mul((4*i)!*i!^2/((2*i)!)^3,i=1..n): end:seq(2^ceil(n/2)*f(floor((n-1)/2))*f(floor(n/2)),n=1..20);
%K nonn
%O 1,1
%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jan 12 2003
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