A015004 q-factorial numbers for q=5.

1, 1, 6, 186, 29016, 22661496, 88515803376, 1728802155736656, 168827903320618878336, 82435457461295106532780416, 201258420458750640859769304304896, 2456767777551003294245070550498298923776, 149949204558598784020761783280669552547300269056

Offset: 0

Author

Olivier Gérard

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..50
• Index entries for sequences related to factorial numbers.

Crossrefs

Column q=5 of A069777.

Cf. A015001, A015002, A015005, A015006, A015007, A015008, A015009, A015011.

Cf. A003463, A100222.

Programs

Magma

[n le 1 select 1 else (5^n-1)*Self(n-1)/4: n in [1..15]]; // Vincenzo Librandi, Oct 25 2012

Mathematica

RecurrenceTable[{a[1]==1, a[n]==((5^n - 1)* a[n-1])/4}, a, {n, 15}] (* Vincenzo Librandi, Oct 25 2012 *)
Table[QFactorial[n, 5], {n, 15}] (* Bruno Berselli, Aug 14 2013 *)

PARI

a(n) = { my(q=5); prod(k=1, n, ((q^k - 1) / (q - 1))) } \\ Andrew Howroyd, Feb 18 2018

Formula

a(n) = Product_{k=1..n} ((q^k - 1) / (q - 1)) where q = 5.

a(0) = 1, a(n) = (5^n-1)*a(n-1)/4. - Vincenzo Librandi, Oct 25 2012

From Amiram Eldar, Jul 05 2025: (Start)

a(n) = Product_{k=1..n} A003463(k).

a(n) ~ c * 5^(n*(n+1)/2)/4^n, where c = A100222. (End)

Extensions

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