A015007 q-factorial numbers for q=8.

1, 1, 9, 657, 384345, 1799118945, 67375205371305, 20185139902805378865, 48378633136349277767794425, 927610024989668734297857360967425, 142287668466497494704440569679875994730825, 174605966461872393482359052970987514818406771638225

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..40
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A015001, A015002, A015004, A015005, A015006, A015008, A015009, A015011.

Column q=8 of A069777.

Cf. A023001, A132036.

Programs

Magma

[n le 1 select 1 else (8^n-1)*Self(n-1)/7: n in [1..15]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((8^n - 1) * a[n-1])/7}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)
Table[QFactorial[n, 8], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} ((q^k - 1) / (q - 1)), with q=8.

a(0) = 1, a(n) = (8^n-1)*a(n-1)/7. - Vincenzo Librandi, Oct 26 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A023001(k).

a(n) ~ c * 8^(n*(n+1)/2)/7^n, where c = A132036. (End)

Extensions

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