A064320 a(n) = Product_{j=1..n} j^C(n-1,j-1).

1, 2, 12, 864, 14929920, 37150418534400000, 10063619980174622195712000000000000000, 664903611914043473202543232567979684173499596800000000000000000000000000000000000

Offset: 1

Author

Henry Bottomley, Sep 10 2001

Keywords

• nonn

Comments

Product variant of binomial transform of natural numbers.

From Benoit Cloitre, Jan 29 2002: (Start)

Array interpretation (first row and column are the natural numbers):

1 2 3 4 .....

2 2 6 12 ....

3 4 12 72 ...

....... 864 ...

(End)

Examples

			a(5) = (1^1)*(2^4)*(3^6)*(4^4)*(5^1) = 1*16*729*256*5 = 14929920.
		

Crossrefs

Cf. A001792. Equals A064319(n, n).

Programs

Maple

A064320:=n->product(i^binomial(n-1,i-1+0^(n-1)), i=1..n): seq(A064320(n), n=1..8); # Wesley Ivan Hurt, Apr 16 2015

Mathematica

Table[Product[j^Binomial[n - 1, j - 1], {j, 1, n}], {n, 8}] (* Michael De Vlieger, Apr 16 2015 *)

PARI

a(n) = prod(j=1, n, j^binomial(n-1,j-1)); \\ Michel Marcus, Apr 17 2015

Formula

Main diagonal of array T(i, 1)=i, T(1, j)=j and T(i, j)=T(i-1, j)*T(i-1, j-1). - Benoit Cloitre, Aug 16 2003, corrected Apr 16 2015