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A078973 Total dimension of the homology of a free 2-step nilpotent Lie algebra of rank n. 0
2, 6, 36, 420, 9800, 452760, 41835024, 7691667984, 2828336198688, 2073619375892064, 3040584296923128384, 8898500292240756664896, 52084270468105185237918848, 608812309050346291991694422400 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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 A152480 A001660
KEYWORD
nonn
AUTHOR
Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Jan 12 2003
STATUS
approved

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Last modified March 19 07:31 EDT 2024. Contains 370955 sequences. (Running on oeis4.)