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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
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 */
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Nov 23 2010
EXTENSIONS
More terms from Alois P. Heinz, Nov 03 2012
STATUS
approved