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In this paper we investigate a class of domains $\Omega^{n+1}_k =\{(z,w)\in\mathbb{C}^n\times \mathbb{C}: |z|^k < |w| < 1\}$ for $k \in \mathbb{Z}^+$which generalizes the Hartogs triangle. we first obtain the new explicitformulas for the Bergman kernel function on these domains and further give arange of $p$ values for which the $L^p$ boundedness of the Bergman projectionholds. This range of $p$ is shown to be sharp.

$L^p$ regularity of the Bergman projection on generalizations of the Hartogs triangle in $\mathbb{C}^{n+1}$