Gf. Armstrong et al., EXPLICIT BETTI NUMBERS FOR A FAMILY OF NILPOTENT LIE-ALGEBRAS, Proceedings of the American Mathematical Society, 125(2), 1997, pp. 381-385
Betti numbers for the Heisenberg Lie algebras were calculated by Santh
aroubane in his 1983 paper. However few other examples have appeared i
n the literature. In this note we give the Betti numbers for a family
of (2n+1)-dimensional 2-step nilpotent extensions of R by R(2n).