A015005 q-factorial numbers for q=6.

1, 1, 7, 301, 77959, 121226245, 1131162092095, 63330372050122765, 21274128570193389587095, 42878835824239014254983869205, 518543838148941095553869851505328175, 37625235473766496167083515195884075739704925, 16380389585902052954270520869620904155598347770499975

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..50
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A015001, A015002, A015004, A015006, A015007, A015008, A015009, A015011.

Column q=6 of A069777.

Cf. A003464, A132034.

Programs

Magma

[n le 1 select 1 else (6^n-1)*Self(n-1)/5: n in [1..15]]; // Vincenzo Librandi, Oct 25 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((6^n - 1) * a[n-1])/5}, a, {n, 15}] (* Vincenzo Librandi, Oct 25 2012 *)
Table[QFactorial[n, 6], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} (6^k-1)/(6-1).

a(0) = 1, a(n) = (6^n-1)*a(n-1)/5. - Vincenzo Librandi, Oct 25 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A003464(k).

a(n) ~ c * 6^(n*(n+1)/2)/5^n, where c = A132034. (End)

Extensions

a(0)=1 prepended by Alois P. Heinz, Sep 08 2021