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  2. Factorial - Wikipedia

    en.wikipedia.org/wiki/Factorial

    In mathematics, the factorial of a non-negative integer, denoted by !, is the product of all positive integers less than or equal to . The factorial of also equals the product of with the next smaller factorial: ! = () = ()! For example, ! =! = =

  3. Double factorial - Wikipedia

    en.wikipedia.org/wiki/Double_factorial

    Stirling permutations, permutations of the multiset of numbers 1, 1, 2, 2, ..., k, k in which each pair of equal numbers is separated only by larger numbers, where k = ⁠ n + 1 / 2 ⁠. The two copies of k must be adjacent; removing them from the permutation leaves a permutation in which the maximum element is k − 1 , with n positions into ...

  4. Factorial number system - Wikipedia

    en.wikipedia.org/wiki/Factorial_number_system

    From this it follows that the rightmost digit is always 0, the second can be 0 or 1, the third 0, 1 or 2, and so on (sequence A124252 in the OEIS).The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS).

  5. Stirling's approximation - Wikipedia

    en.wikipedia.org/wiki/Stirling's_approximation

    [1] [2] [3] One way of stating the approximation involves the logarithm of the factorial: ⁡ (!) = ⁡ + (⁡), where the big O notation means that, for all sufficiently large values of , the difference between ⁡ (!

  6. Gamma function - Wikipedia

    en.wikipedia.org/wiki/Gamma_function

    8.2 19th century: Gauss, Weierstrass ... The simple formula for the factorial, x! = 1 × 2 × ⋯ × x is only valid when x is a positive integer, ... equals any of ...

  7. Factorion - Wikipedia

    en.wikipedia.org/wiki/Factorion

    In number theory, a factorion in a given number base is a natural number that equals the sum of the factorials of its digits. [ 1 ] [ 2 ] [ 3 ] The name factorion was coined by the author Clifford A. Pickover .

  8. American Tower (AMT) Q4 2024 Earnings Call Transcript - AOL

    www.aol.com/american-tower-amt-q4-2024-174513856...

    In Q4, we opportunistically addressed a portion of our 2025 debt refinancing needs, successfully issuing $1.2 billion in senior unsecured notes at an average coupon of 5.2% and average tenor of 7. ...

  9. Power of two - Wikipedia

    en.wikipedia.org/wiki/Power_of_two

    The only known powers of 2 with all digits even are 2 1 = 2, 2 2 = 4, 2 3 = 8, 2 6 = 64 and 2 11 = 2048. [12] The first 3 powers of 2 with all but last digit odd is 2 4 = 16, 2 5 = 32 and 2 9 = 512. The next such power of 2 of form 2 n should have n of at least 6 digits.