ABSTRACT
C0a = 1, Cka = (a k
) =
a(a – 1) . . . (a – k + 1) k!
, where k = 1, 2, . . .
◮ Generalization. Some properties. General case:
Cba = Γ(a + 1)
Γ(b + 1)Γ(a – b + 1) , where Γ(x) is the gamma function. Properties:
C0a = 1, Ckn = 0 for k = –1, –2, . . . or k > n,
Cb+1a = a
b + 1 Cba-1 =
a – b
b + 1 Cba, C
Cn2n = (–1)n (2n – 1)!!
