OFFSET
1,2
COMMENTS
Defining a partial multiplication by nm = "n choose m" (where n+1>m) this is simply (...((((n)(n-1))(n-2))(n-3)...)3)2)1. With the brackets ordered in the opposite direction, as in: n((n-1)((n-2)....(3(2(1)))...)), is obviously simply n.
FORMULA
a(n) = (...(((n choose n-1) choose n-2) choose n-3)... choose 2) choose 1
EXAMPLE
E.g. a(5)=45 because 5C4=5 and then 5C3=10 and then 10C2=45 and finally 45C1=45.
MATHEMATICA
b[n_, k_] := Binomial[n, k]; b[n_, k_] /; k == n-1 := n ; b[n_, k_] /; k == n-2 := n(n-1)/2; b[n_, k_] /; k == n-3 := n(n-1)(n-2)/6; a[n_] := Fold[b[#1, #1 - #2] &, n, Range[n-1, 1, -1]]; Table[a[n], {n, 1, 8}] (* Jean-François Alcover, Dec 16 2011 *)
CROSSREFS
KEYWORD
nonn,nice,easy
AUTHOR
Marcel Jackson (Marcel.Jackson(AT)utas.edu.au)
STATUS
approved