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.

A092300 a(n) = 2*5^(n^2+2n+1)*Product_{j=1..n} (25^j-1).

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%I A092300 #10 Jul 07 2025 03:32:19
%S A092300 10,30000,58500000000,71406562500000000000,
%T A092300 54478744277343750000000000000000,
%U A092300 25977486943588417053222656250000000000000000000,7741894375438878098811060190200805664062500000000000000000000000,1442040200190701731357565969692841463256627321243286132812500000000000000000000000000
%N A092300 a(n) = 2*5^(n^2+2n+1)*Product_{j=1..n} (25^j-1).
%C A092300 The order of the p-Clifford group for an odd prime p is a*p^(n^2+2n+1)*Product_{j=1..n} (p^(2*j)-1), where a = gcd(p+1,4).
%H A092300 G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.
%F A092300 From _Amiram Eldar_, Jul 07 2025: (Start)
%F A092300 a(n) = 2 * A089989(n).
%F A092300 a(n) ~ c * 5^(2*n^2+3*n+1), where c = 2 * Product_{k>=1} (1 - 1/5^(2*k)) = 1.916800205127... . (End)
%t A092300 a[n_] := 2*5^(n^2+2*n+1) * Product[25^j - 1, {j, 1, n}]; Array[a, 10, 0] (* _Amiram Eldar_, Jul 07 2025 *)
%Y A092300 Cf. A001309, A003956.
%Y A092300 Cf. A092299 and A092301 (p=3), A092300 and A089989 (p=5), A090768 and A090769 (p=7), A090770 (p=2, although this is the wrong formula in that case).
%K A092300 nonn
%O A092300 0,1
%A A092300 _N. J. A. Sloane_, Feb 10 2004