OFFSET
1,2
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)
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
EXAMPLE
a(5) = (1^1)*(2^4)*(3^6)*(4^4)*(5^1) = 1*16*729*256*5 = 14929920.
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 *)
PROG
(PARI) a(n) = prod(j=1, n, j^binomial(n-1, j-1)); \\ Michel Marcus, Apr 17 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Sep 10 2001
STATUS
approved