A049383 Iterated binomial coefficients.

1, 2, 3, 6, 45, 103285, 637700839095606788040, 47907611227303520484704817869777341656612683981478793109229998610027375657813231974364873146104781203691314770

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.

Links

Table of n, a(n) for n=1..8.

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

Cf. A000142.

Sequence in context: A127315 A018359 A274805 * A099411 A018372 A097350

Adjacent sequences: A049380 A049381 A049382 * A049384 A049385 A049386

Keyword

nonn,nice,easy

Author

Marcel Jackson (Marcel.Jackson(AT)utas.edu.au)

Status

approved