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A182607 Number of conjugacy classes in GL(n,16). 17
1, 15, 255, 4080, 65520, 1048305, 16776960, 268431105, 4294962960, 68719407120, 1099511558160, 17592184926480, 281474975596815, 4503599609479680, 72057594020040960, 1152921504320590335, 18446744073423298800, 295147905174771671280, 4722366482865065107440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..250

FORMULA

G.f.: Product_{k>=1} (1-x^k)/(1-16*x^k). - Alois P. Heinz, Nov 03 2012

MAPLE

with (numtheory):

b:= proc(n) b(n):= add(phi(d)*16^(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]*16^(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>6: */ [1] cat [NumberOfClasses(GL(n, 16)) : n in [1..6]];

(PARI)

N=66; x='x+O('x^N);

gf=prod(n=1, N, (1-x^n)/(1-16*x^n)  );

v=Vec(gf)

/* Joerg Arndt, Jan 24 2013 */

CROSSREFS

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182608, A182609, A182610, A182611, A182612.

Sequence in context: A218368 A123816 A273921 * A218284 A218634 A218238

Adjacent sequences:  A182604 A182605 A182606 * A182608 A182609 A182610

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 18 17:56 EST 2017. Contains 294894 sequences.