A015006 q-factorial numbers for q=7.

1, 1, 8, 456, 182400, 510902400, 10017774259200, 1375009641495014400, 1321109263548409835520000, 8885253784030448738183147520000, 418310711031156574478261944188764160000, 137856159231156714984163673320892478249861120000

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, A015007, A015008, A015009, A015011.

Column q=7 of A069777.

Cf. A023000, A132035.

Programs

Magma

[n le 1 select 1 else (7^n-1)*Self(n-1)/6: n in [1..15]]; // Vincenzo Librandi, Oct 25 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((7^n - 1) * a[n-1])/6}, a, {n, 15}] (* Vincenzo Librandi, Oct 25 2012 *)
Table[QFactorial[n, 7], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} (7^k-1)/(7-1).

a(0) = 1, a(n) = (7^n - 1)*a(n-1)/6. - Vincenzo Librandi, Oct 25 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A023000(k).

a(n) ~ c * 7^(n*(n+1)/2)/6^n, where c = A132035. (End)

Extensions

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