[math-fun] about Eulerian numbers 2^n-n-1

hi all, is it evident that A000295 in EIS, defined as in title, also equals the exponent of 2 in (2^n-1)! as calculated by Table[ pow[ 2^n - 1 , 2], {n, 29} ] using pow[ nfac_ , p_] := (nfac - Plus @@ IntegerDigits[ nfac, p ])/(p - 1) not earth-shaking, just in need of 'sanity check' Wouter.