cp's OEIS Frontend

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

%I A064320 #28 Mar 03 2020 01:30:52
%S A064320 1,2,12,864,14929920,37150418534400000,
%T A064320 10063619980174622195712000000000000000,
%U A064320 664903611914043473202543232567979684173499596800000000000000000000000000000000000
%N A064320 a(n) = Product_{j=1..n} j^C(n-1,j-1).
%C A064320 Product variant of binomial transform of natural numbers.
%C A064320 From _Benoit Cloitre_, Jan 29 2002: (Start)
%C A064320 Array interpretation (first row and column are the natural numbers):
%C A064320 1   2   3   4 .....
%C A064320 2   2   6  12 ....
%C A064320 3   4  12  72 ...
%C A064320 .......   864 ...
%C A064320 (End)
%F A064320 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
%e A064320 a(5) = (1^1)*(2^4)*(3^6)*(4^4)*(5^1) = 1*16*729*256*5 = 14929920.
%p A064320 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
%t A064320 Table[Product[j^Binomial[n - 1, j - 1], {j, 1, n}], {n, 8}] (* _Michael De Vlieger_, Apr 16 2015 *)
%o A064320 (PARI) a(n) = prod(j=1, n, j^binomial(n-1,j-1)); \\ _Michel Marcus_, Apr 17 2015
%Y A064320 Cf. A001792. Equals A064319(n, n).
%K A064320 nonn
%O A064320 1,2
%A A064320 _Henry Bottomley_, Sep 10 2001