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The fifteen different rooted binary trees (with unordered children) on a set of four labeled leaves, illustrating 15 = (2 × 4 − 3)‼ (see article text). Double factorials are motivated by the fact that they occur frequently in enumerative combinatorics and other settings. For instance, n‼ for odd values of n counts
As one special case, it can be used to prove that if n is a positive integer then 4 divides () if and only if n is not a power of 2. It follows from Legendre's formula that the p -adic exponential function has radius of convergence p − 1 / ( p − 1 ) {\displaystyle p^{-1/(p-1)}} .
15.2x8.4x2.25 cm, 6"×3+3/8"x7/8" The fx-39 is a scientific calculator manufactured by Casio released in 1978 [ 1 ] and is one of several models to share the same physical design format. Display
2: 2 3: 6 4: 24 5: 120 6: 720 7: 5 040: 8: 40 320: 9: ... a 1975 calculator with a factorial key ... Divide all of the exponents by two (rounding down to an integer ...
2.4 Modified-factorial denominators. 2.5 Binomial coefficients. 2.6 Harmonic numbers. 3 Binomial coefficients. 4 Trigonometric functions. 5 Rational functions.
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
Here is a sample program that computes the factorial of an integer number from 2 to 69 (ignoring the calculator's built-in factorial/gamma function). There are two versions of the example: one for algebraic mode and one for RPN mode. The RPN version is significantly shorter. Algebraic version:
Multiplicative partitions of factorials are expressions of values of the factorial function as products of powers of prime numbers. They have been studied by Paul Erdős and others. [1] [2] [3] The factorial of a positive integer is a product of decreasing integer factors, which can in turn be factored into prime numbers.