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A182605 Number of conjugacy classes in GL(n,11). 18
1, 10, 120, 1320, 14630, 160920, 1771440, 19485720, 214357440, 2357931730, 25937408640, 285311493720, 3138428201160, 34522710196920, 379749831637440, 4177248147997440, 45949729842155150, 505447028263532520, 5559917313256631160, 61159090445821012920 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: Product_{k>=1} (1-x^k)/(1-11*x^k). - Alois P. Heinz, Nov 03 2012
MAPLE
with(numtheory):
b:= proc(n) b(n):= add(phi(d)*11^(n/d), d=divisors(n))/n-1 end:
a:= proc(n) a(n):= `if`(n=0, 1,
add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Nov 03 2012
MATHEMATICA
b[n_] := Sum[EulerPhi[d]*11^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *)
PROG
(Magma) N := 300; R<x> := PowerSeriesRing(Integers(), N);
Eltseq( &*[ (1-x^k)/(1-11*x^k) : k in [1..N] ] ); // Volker Gebhardt, Dec 07 2020
(PARI)
N=66; x='x+O('x^N);
gf=prod(n=1, N, (1-x^n)/(1-11*x^n) );
v=Vec(gf)
/* Joerg Arndt, Jan 24 2013 */
CROSSREFS
Sequence in context: A307620 A300522 A252874 * A024127 A005949 A027568
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 23 2010
EXTENSIONS
More terms from Alois P. Heinz, Nov 03 2012
STATUS
approved

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Last modified March 29 09:42 EDT 2024. Contains 371268 sequences. (Running on oeis4.)