Boolean-Eulerian numbers count red-blue colored decreasing binary trees and equal 2^{n-1} times the nth Euler number; their polynomials are algebraic transforms of Eulerian polynomials that inherit gamma-positivity, real-rootedness, and zero interlacing.
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Boolean--Eulerian numbers
Boolean-Eulerian numbers count red-blue colored decreasing binary trees and equal 2^{n-1} times the nth Euler number; their polynomials are algebraic transforms of Eulerian polynomials that inherit gamma-positivity, real-rootedness, and zero interlacing.