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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

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: A089709 A262234 A055512 * A208650 A152480 A001660

Adjacent sequences:  A078970 A078971 A078972 * A078974 A078975 A078976

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 12 11:55 EDT 2021. Contains 343821 sequences. (Running on oeis4.)