A015008 q-factorial numbers for q=9.

1, 1, 10, 910, 746200, 5507702200, 365876657146000, 218747042884536166000, 1177042838234827583459440000, 57001313848230245122464621625840000, 24843911488189148287648216529610193612000000, 97453533413342456299179976631323547842824103012000000

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, A015007, A015009, A015011.

Column q=9 of A069777.

Cf. A002452, A132037.

Programs

Magma

[n le 1 select 1 else (9^n - 1)*Self(n-1)/8: n in [1..15]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((9^n - 1) * a[n-1])/8}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)
Table[QFactorial[n, 9], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} (9^k - 1) / (9 - 1).

a(0) = 1, a(n) = (9^n - 1)*a(n-1)/8. - Vincenzo Librandi, Oct 26 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A002452(k).

a(n) ~ c * 3^(n*(n+1))/8^n, where c = A132037. (End)

Extensions

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