A220790 Product(6^n - 6^k, k=0..n-1).

1, 5, 1050, 8127000, 2273284440000, 22906523331216000000, 8310241106635054164480000000, 108537128570336598656772717772800000000, 51032497739317419104816901041614046625792000000000

Offset: 0

Author

Vincenzo Librandi, Jan 28 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..35

Crossrefs

Cf. A027873, A109354.

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).

Programs

Magma

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

Magma

/* By the second formula: */
m:=9;
A109354 := [6^(n*(n-1) div 2): n in [0..m-1]];
A027873 := [1] cat [&*[6^i-1: i in [1..n]]: n in [1..m]];
[A109354[i]*A027873[i]: i in [1..m]]; // Bruno Berselli, Jan 30 2013

Mathematica

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

Formula

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

a(n) = A109354(n)*A027873(n). - Bruno Berselli, Jan 30 2013