Reading between the lines - Could Euler have made use of Wallis’s Tables of Interpolations to determine the value of 1/2!?

In 1738 Leonhard Euler wrote a paper on the use of integrals to both quantify and provide a proof for (1/2)!, being a value to interpolate the sequence of the positive integer factorials. It was these findings that became the foundation for the subsequent generation of Euler’s Gamma “Γ” Function. Euler had been aware the integral Int dx(-ln x)^1/2 equated to (SQRT Pi)/2, , but he needed to prove this also represented the interpolation value for (1/2)!.As is summarised in this paper, his method of proof had been to construct a second integral formula which, although linking to the one above, produced, on expansion plus gross-up, a fraction involving two product series of positive integers. Euler then interpolated both these series and solved by matching the interpolation fraction to a known output from trigonometric substitution of that second integral, when its index had been set to 1/2.In this way Euler computed the value for (1/2)! to be (SQRT Pi)/2.HOWEVER, Euler could have achieved this value by using the pre-calculus interpolation tables generated by John Wallis some 80 years previously. This is because Euler’s integral expansion and gross-up merely generated the fractional sequences equal to (n!)²/(2n!) for the positive integer values of n. Furthermore, Euler should have noticed these fractional sequences produce single fractions for each positive integer value of n, which equate to the reciprocals of a Wallis sequence 1, 2, 6, 20, 70…, being a sequence that Wallis himself had already interpolated.Hence, although Euler’s work is extremely important when considering the Γ Function, one finds his interpolation work merely confirms a previous finding of Wallis. It is my belief Euler could have given a lot more credit to the work of Wallis, instead of just his passing reference to another of Wallis’s significant outputs, being that of the infinite product formula for pi.