A078973 Total dimension of the homology of a free 2-step nilpotent Lie algebra of rank n.

2, 6, 36, 420, 9800, 452760, 41835024, 7691667984, 2828336198688, 2073619375892064, 3040584296923128384, 8898500292240756664896, 52084270468105185237918848, 608812309050346291991694422400

Offset

1,1

Links

Table of n, a(n) for n=1..14.

J. Grassberger, A. King, P. Tirao, On the homology of free 2-step nilpotent Lie algebras, J. Algebra 254 (2002), 213-225.

Formula

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.

a(n) ~ K*2^(n^2/2)*n^(1/8), where K=1.3814... - Nordine Fahssi, Jan 17 2019

From Jon E. Schoenfield, Jan 17 2019: (Start)

K = 1.38143139396100192327615434710888289668811010590733/

41912628937302462176044631403587011199108546012939...

(End)

Maple

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);

Crossrefs

Sequence in context: A262234 A371043 A055512 * A208650 A374453 A152480

Adjacent sequences: A078970 A078971 A078972 * A078974 A078975 A078976

Keyword

nonn

Author

Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jan 12 2003

Status

approved