A015009 q-factorial numbers for q=10.

1, 1, 11, 1221, 1356531, 15072415941, 1674711207620451, 1860790044610366931061, 20675444733360738721748118771, 2297271634742810443154153338805764581, 2552524038347870310755413660544832496799359491, 28361378203581611893021499527080870668821235178133404501

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, A015008, A015011.

Column q=10 of A069777.

Cf. A002275, A132038.

Programs

Magma

[n le 1 select 1 else (10^n-1)*Self(n-1)/9: n in [1..15]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((10^n-1) * a[n-1])/9}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)
Table[QFactorial[n, 10], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} (q^k - 1)/(q - 1) with q=10.

a(0) = 1, a(n) = (10^n - 1)*a(n-1)/9. - Vincenzo Librandi, Oct 26 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A002275(k).

a(n) ~ c * 10^(n*(n+1)/2)/9^n, where c = A132038. (End)

Extensions

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