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Graphico: factoriales del numeros 1-5 Le factorial [ 1] numero natural attribue le producto de omne numeros de 1 usque iste numero incluse. Iste producto es representate per un puncto de exclamation postponite. Iste notation es originari del mathematico alsatian Christian Kramp (1760–1826).
Su definition es
n
!
:=
∏
i
=
1
n
i
{\displaystyle n!:=\prod _{i=1}^{n}i}
0
!
:=
1
1
!
=
1
=
1
2
!
=
1
?
2
=
2
3
!
=
1
?
2
?
3
=
6
4
!
=
1
?
2
?
3
?
4
=
24
5
!
=
1
?
2
?
3
?
4
?
5
=
120
6
!
=
1
?
2
?
3
?
4
?
5
?
6
=
720
7
!
=
1
?
2
?
3
?
4
?
5
?
6
?
7
=
5
′
040
8
!
=
1
?
2
?
3
?
4
?
5
?
6
?
7
?
8
=
40
′
320
9
!
=
1
?
2
?
3
?
4
?
5
?
6
?
7
?
8
?
9
=
362
′
880
{\displaystyle {\begin{array}{rll}0!&:=1&\\1!&=1&=1\\2!&=1\cdot 2&=2\\3!&=1\cdot 2\cdot 3&=6\\4!&=1\cdot 2\cdot 3\cdot 4&=24\\5!&=1\cdot 2\cdot 3\cdot 4\cdot 5&=120\\6!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6&=720\\7!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7&=5'040\\8!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8&=40'320\\9!&=1\cdot 2\cdot 3\cdot 4\cdot 5\cdot 6\cdot 7\cdot 8\cdot 9&=362'880\end{array}}}
Le plus grande parte del calculatores electronic pote indicar maximalmente
69
!
{\displaystyle 69!}
69
!
{\displaystyle 69!}
Le duple factorial o semifactorial se nota
n
!
!
{\displaystyle n!!}
n
{\displaystyle n}
n
!
!
=
{
1
si
n
=
0
o
n
=
1
,
n
?
(
n
?
2
)
!
!
si
n
≥
2.
{\displaystyle n!!={\begin{cases}1&{\text{si }}n=0{\text{ o }}n=1,\\n\cdot (n-2)!!&{\text{si }}n\geq 2.\end{cases}}}
per exemplo
8
!
!
=
8
?
6
?
4
?
2
=
384
{\displaystyle 8!!=8\cdot 6\cdot 4\cdot 2=384}
9
!
!
=
9
?
7
?
5
?
3
?
1
=
945
{\displaystyle 9!!=9\cdot 7\cdot 5\cdot 3\cdot 1=945}
n
=
0
,
1
,
2
,
…
{\displaystyle n=0,1,2,\dots }
[ 2]
1
,
1
,
2
,
3
,
8
,
15
,
48
,
105
,
384
,
945
,
3
′
840
,
…
{\displaystyle 1,1,2,3,8,15,48,105,384,945,3'840,\dots }
↑
Derivation (in ordine alphabetic):
(ca ) Factorial ||
(de) Fakult?t (Mathematik) ||
(en) (es) (fr) (it) (pt) (ro ) Factorial
|| (ru) Факториал
↑ Patrono:OEIS
