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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-François 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: A167870 A358114 A097192 * A331322 A126153 A002553 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 March 24 07:38 EDT 2023. Contains 361454 sequences. (Running on oeis4.)