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A182611 Number of conjugacy classes in GL(n,25). 17
1, 24, 624, 15600, 390600, 9764976, 244140000, 6103499376, 152587874400, 3814696859400, 95367431234400, 2384185780844400, 59604644765235024, 1490116119130470000, 37252902984364860000, 931322574609121110624, 23283064365380605500600, 582076609134515127375600 (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)/(1-25*x^k). - Alois P. Heinz, Nov 03 2012

MAPLE

with (numtheory):

b:= proc(n) b(n):= add(phi(d)*25^(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]*25^(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>4: */ [1] cat [NumberOfClasses(GL(n, 25)) : n in [1..4]];

(PARI)

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

gf=prod(n=1, N, (1-x^n)/(1-25*x^n)  );

v=Vec(gf)

/* Joerg Arndt, Jan 24 2013 */

CROSSREFS

Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182610, A182612.

Sequence in context: A144348 A167870 A097192 * A126153 A002553 A006201

Adjacent sequences:  A182608 A182609 A182610 * A182612 A182613 A182614

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 23 2013

STATUS

approved

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Last modified November 18 18:46 EST 2017. Contains 294894 sequences.