Passer au contenu principal

Accueil / Mathematics (thesaurus)

Mathematics (thesaurus)

... > calculus > sequence > integer sequence > factorial > alternating factorial

mathematical analysis > combinatorics > factorial > alternating factorial

algebra > combinatorics > factorial > alternating factorial

number > number theory > arithmetic function > factorial > alternating factorial

Terme préférentiel

alternating factorial

In mathematics, an alternating factorial is the absolute value of the alternating sum of the first n factorials of positive integers. This is the same as their sum, with the odd-indexed factorials multiplied by −1 if n is even, and the even-indexed factorials multiplied by −1 if n is odd, resulting in an alternation of signs of the summands (or alternation of addition and subtraction operators, if preferred). To put it algebraically,
${\\displaystyle \\operatorname {af} (n)=\\sum _{i=1}^{n}(-1)^{n-i}i!}$
or with the recurrence relation
${\\displaystyle \\operatorname {af} (n)=n!-\\operatorname {af} (n-1)}$
in which af(1) = 1. The first few alternating factorials are
1, 1, 5, 19, 101, 619, 4421, 35899, 326981, 3301819, 36614981, 442386619, 5784634181, 81393657019 (sequence A005165 in the OEIS)

(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Alternating_factorial)

factorial

factorielle alternante

français

URI

http://data.loterre.fr/ark:/67375/PSR-JMDZ85Q6-X

Télécharger ce concept :

RDF/XML TURTLE JSON-LD Date de création 24/08/2023, dernière modification le 18/10/2024