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A182605 Number of conjugacy classes in GL(n,11). 17
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

Alois P. Heinz, Table of n, a(n) for n = 0..300

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-Fran├žois Alcover, Feb 17 2014, after Alois P. Heinz *)

PROG

(MAGMA) /* The program does not work for n>5: */ [1] cat [NumberOfClasses(GL(n, 11)): n in [1..6]];

(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

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182606, A182607, A182608, A182609, A182610, A182611, A182612.

Sequence in context: A069498 A226767 A252874 * A024127 A005949 A027568

Adjacent sequences:  A182602 A182603 A182604 * A182606 A182607 A182608

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Nov 23 2010

EXTENSIONS

More terms from Alois P. Heinz, Nov 03 2012

MAGMA code edited by Vincenzo Librandi, Jan 24 2013

STATUS

approved

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Last modified November 23 19:03 EST 2017. Contains 295128 sequences.