A015011 q-factorial numbers for q=11.

1, 1, 12, 1596, 2336544, 37630041120, 6666387564654720, 12990902775831251994240, 278471536921607824648305285120, 65662131721505488121539650946349537280, 170310659060181679663863033233125976844488908800, 4859161865915056755501262525796512204608930674134393036800

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, A015009.

Column q=11 of A069777.

Cf. A016123, A132267.

Programs

Magma

[n le 1 select 1 else (11^n-1)*Self(n-1)/10: n in [1..15]]; // Vincenzo Librandi, Oct 26 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((11^n - 1) * a[n-1])/10}, a, {n, 15}] (* Vincenzo Librandi, Oct 26 2012 *)
Table[QFactorial[n, 11], {n, 11}] (* Bruno Berselli, Aug 14 2013 *)

Formula

a(n) = Product_{k=1..n} (11^k - 1) / (11 - 1).

a(0) = 1, a(n) = (11^n - 1)*a(n-1)/10. - Vincenzo Librandi, Oct 26 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A016123(k-1).

a(n) ~ c * 11^(n*(n+1)/2)/10^n, where c = A132267. (End)

Extensions

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