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2.1 Factorial of zero. 3 ... , is the product of all positive integers less than or equal to ... is the sequence of initial digits of some factorial number in that ...
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 .
For arbitrarily greater numbers one has to choose a base for representing individual digits, say decimal, and provide a separating mark between them (for instance by subscripting each digit by its base, also given in decimal, like 2 4 0 3 1 2 0 1, this number also can be written as 2:0:1:0!). In fact the factorial number system itself is not ...
The simple formula for the factorial, x! = 1 × 2 × ⋯ × x is only ... [1] If the real part of the complex number ... except integers less than or equal to zero ...
A googol is the large number 10 100 or ten to the power of one hundred. ... it would still only equal 10 95 ... (factorial of 70). Using an integral, binary ...
[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 (!
The number of derangements of a set of size n is known as the subfactorial of n or the n th derangement number or n th de Montmort number (after Pierre Remond de Montmort). Notations for subfactorials in common use include !n, D n, d n, or n¡ . [a] [1] [2] For n > 0 , the subfactorial !n equals the nearest integer to n!/e, where n!
The number of such "sorted multiplicative partitions" of ! grows with , and is given by the sequence 1, 1, 3, 3, 10, 10, 30, 75, 220, 220, 588, 588, 1568, 3696, 11616, ... (sequence A085288 in the OEIS). Not all sorted multiplicative partitions of a given factorial have the same length.