cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A003831 Order of universal Chevalley group D_n (4).

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%I A003831 #20 Jul 08 2025 07:50:31
%S A003831 3,3600,987033600,67010895544320000,1154606796534757164318720000,
%T A003831 5081732431326820541485324550799360000000,
%U A003831 5722569627753465177061732369386833143098255605760000000,1649493899207759406688161287839326786813727965837588934265143296000000000
%N A003831 Order of universal Chevalley group D_n (4).
%D A003831 J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
%D A003831 H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
%H A003831 <a href="/index/Gre#groups">Index entries for sequences related to groups</a>.
%F A003831 a(n) = D(4,n) where D(q,n) is defined in A003830. - _Sean A. Irvine_, Sep 17 2015
%F A003831 a(n) ~ c * 4^(n*(2*n-1)), where c = Product_{k>=1} (1 - 1/4^(2*k)) = 0.933594707399... . - _Amiram Eldar_, Jul 08 2025
%p A003831 a:= n -> 4^(n*(n-1))*(4^n-1)*mul(4^(2*k)-1, k=1..n-1):
%p A003831 seq(a(n), n=1..8);  # _Alois P. Heinz_, Jun 24 2025
%t A003831 d[q_, n_] := q^(n*(n-1)) * (q^n-1) * Product[q^(2*k) - 1, {k, 1, n-1}]; Table[d[4, n], {n, 1, 8}] (* _Amiram Eldar_, Jun 24 2025 *)
%Y A003831 Cf. A003830, A003832, A003834, A003835, A003836.
%K A003831 nonn,easy
%O A003831 1,1
%A A003831 _N. J. A. Sloane_