A028681 Galois numbers for p=19; order of group AGL(n,19).

1, 342, 44446320, 2090711424299040, 35507456811518119000588800, 217698482437446717711443628892666137600, 481835288795046555242155407852974930874821656470528000, 384989616762670041552999657317996225002975219911214265653201810077696000

Offset: 0

Author

Olivier Gérard

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..27
• Index entries for sequences related to groups.

Crossrefs

Cf. A028365, A028665, A028667, A028669, A028673, A028675, A028679, A028685.

Programs

Mathematica

FoldList[ #1*19^#2 (19^#2-1)&, 1, Range[ 20 ] ]
a[n_] := 19^n * Product[19^n - 19^k, {k, 0, n-1}]; Array[a, 10, 0] (* Amiram Eldar, Jul 12 2025 *)

PARI

a(n) = 19^n * prod(k = 0, n-1, 19^n - 19^k); \\ Amiram Eldar, Jul 12 2025

Formula

a(n) = 19^n * Product_{k=0..n-1} (19^n - 19^k).

a(n) ~ c * 19^(n^2+n), where c = Product_{k>=1} (1 - 1/19^k) = 0.944598742929... . - Amiram Eldar, Jul 12 2025