Stieltjes moment properties and continued fractions from combinatorial triangles

Many combinatorial numbers can be placed in the following generalized triangular array [ T n , k ] ? 0 satisfying recurrence relation: = ? ( a + 1 2 ) ? b d with and unless ? for suitable . For denote by q generating function of -th row. In this paper, we develop various criteria x -Stieltjes moment property 3- -log-convexity based on Jacobi continued fraction expression ? t where is set indeterminates consisting those parameters occurring relation. With help criterion Wang Zhu (2016) [36] show that corresponding linear transformation preserves Stieltjes properties sequences. Finally, present some related examples including factorial numbers, Whitney Stirling permutations, minimax trees peak statistics.