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A049315
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The number k(GL(n,q)) of conjugacy classes in GL(n,q), q=5.
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23
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1, 4, 24, 120, 620, 3096, 15600, 77976, 390480, 1952380, 9764880, 48824280, 244136904, 1220683800, 6103496400, 30517481424, 152587794020, 762938966520, 3814696782120, 19073483892120, 95367429207720, 476837146020720, 2384185778835696, 11920928894086200
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OFFSET
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0,2
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REFERENCES
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V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
W. Feit and N. J. Fine, Pairs of commuting matrices over a finite field. Duke Math. Journal, 27 (1960) 91-94.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..450
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FORMULA
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The number a(n) of conjugacy classes in the group GL(n, q) is the coefficient of t^n in the infinite product: product k=1, 2, ... (1-t^k)/(1-qt^k) - Noam Katz (noamkj(AT)hotmail.com), Mar 30 2001.
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MAPLE
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with (numtheory):
b:= proc(n) b(n):= add(phi(d)*5^(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
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PROG
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(MAGMA) /* The program does not work for n>8: */ [1] cat [NumberOfClasses(GL(n, 5)) : n in [1..8]]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
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CROSSREFS
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Cf. A006951, A006952, A049314, A049316.
Sequence in context: A067312 A017976 A002011 * A098224 A024049 A103455
Adjacent sequences: A049312 A049313 A049314 * A049316 A049317 A049318
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KEYWORD
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nonn,changed
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AUTHOR
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Vladeta Jovovic
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EXTENSIONS
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Magma code edited by Vincenzo Librandi, Jan 23 2013
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STATUS
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approved
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