%I #31 Sep 08 2022 08:46:04

%S 1,5,1050,8127000,2273284440000,22906523331216000000,

%T 8310241106635054164480000000,108537128570336598656772717772800000000,

%U 51032497739317419104816901041614046625792000000000

%N Product(6^n - 6^k, k=0..n-1).

%H Vincenzo Librandi, <a href="/A220790/b220790.txt">Table of n, a(n) for n = 0..35</a>

%F a(n) = (6^n - 1)*(6^n - 6)*...*(6^n - 6^(n-1)) for n>0, a(0)=1.

%F a(n) = A109354(n)*A027873(n). - _Bruno Berselli_, Jan 30 2013

%t Table[Product[6^n - 6^k, {k, 0, n-1}], {n, 0, 60}]

%o (Magma)

%o [1] cat [&*[(6^n - 6^k): k in [0..n-1]]: n in [1..8]]; // _Bruno Berselli_, Jan 28 2013

%o (Magma) /* By the second formula: */

%o m:=9;

%o A109354 := [6^(n*(n-1) div 2): n in [0..m-1]];

%o A027873 := [1] cat [&*[6^i-1: i in [1..n]]: n in [1..m]];

%o [A109354[i]*A027873[i]: i in [1..m]]; // _Bruno Berselli_, Jan 30 2013

%Y Cf. A027873, A109354.

%Y Sequences given by product(m^n-m^k, k=0..n-1): A002884 (m=2), A053290 (m=3), A053291 (m=4), A053292 (m=5), A053293 (m=7), A052496 (m=8), A052497 (m=9), A052498 (m=11).

%K nonn,easy

%O 0,2

%A _Vincenzo Librandi_, Jan 28 2013