About the number of vines and regular vines on n nodes

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Copula variational inference (2015, background): “However, their multivariate extensions do not flexibly model dependencies in higher dimensions [4].”
Truncated regular vines in high dimensions with application to financial data (2012, background): “The number of different possible R-vines in d dimensions is very large (Morales-Napoles et al. 2010).”
Pair-Copula Constructions of Multivariate Copulas (2010, background): “For regular vine tr e s the number is even larger (see [49]).”
Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50 (2013, background): “× 2(d−22 ) in d dimensions as shown in Morales-Nápoles et al. (2010).”
Nonparametric estimation of simplified vine copula models: comparison of methods (2017, background): “This choice is very difficult, since there are d!/2 × d(d−2)(d−3)/2 possible vine structures (Morales-Nápoles et al., 2011), which grows excessively with d.”
Selecting and estimating regular vine copulae and application to financial returns (2012, background): “One reason for this is the enormous number of possible R-vine tree sequences (see Morales-N´apoles et al. (2010)) to choose from.”
Selection strategies for regular vine copulae (2013, background): “Since the number of regular vines is very large ([Morales-Nápoles et al., 2010]) it is vital to develop efﬁcient selection strategies for all components of a vine speciﬁcation.”