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A182605 Number of conjugacy classes in GL(n,11).

%I A182605 #28 Jun 19 2023 09:05:46
%S A182605 1,10,120,1320,14630,160920,1771440,19485720,214357440,2357931730,
%T A182605 25937408640,285311493720,3138428201160,34522710196920,
%U A182605 379749831637440,4177248147997440,45949729842155150,505447028263532520,5559917313256631160,61159090445821012920
%N A182605 Number of conjugacy classes in GL(n,11).
%H A182605 Alois P. Heinz, <a href="/A182605/b182605.txt">Table of n, a(n) for n = 0..300</a>
%F A182605 G.f.: Product_{k>=1} (1-x^k)/(1-11*x^k). - _Alois P. Heinz_, Nov 03 2012
%p A182605 with(numtheory):
%p A182605 b:= proc(n) b(n):= add(phi(d)*11^(n/d), d=divisors(n))/n-1 end:
%p A182605 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182605        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182605     end:
%p A182605 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 03 2012
%t A182605 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_ *)
%o A182605 (Magma) N := 300;  R<x> := PowerSeriesRing(Integers(), N);
%o A182605 Eltseq( &*[ (1-x^k)/(1-11*x^k) : k in [1..N] ] ); // _Volker Gebhardt_, Dec 07 2020
%o A182605 (PARI)
%o A182605 N=66; x='x+O('x^N);
%o A182605 gf=prod(n=1,N, (1-x^n)/(1-11*x^n)  );
%o A182605 v=Vec(gf)
%o A182605 /* _Joerg Arndt_, Jan 24 2013 */
%Y A182605 Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182606, A182607, A182608, A182609, A182610, A182611, A182612.
%K A182605 nonn
%O A182605 0,2
%A A182605 _Klaus Brockhaus_, Nov 23 2010
%E A182605 More terms from _Alois P. Heinz_, Nov 03 2012