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A382910 a(n) = A003266(n)^2.

%I A382910 #35 Aug 18 2025 02:12:57
%S A382910 1,1,1,4,36,900,57600,9734400,4292870400,4962558182400,
%T A382910 15011738501760000,118907980672440960000,2465675887223735746560000,
%U A382910 133859078241489389944995840000,19025256931384645503492313743360000,7079298104168226591849489943904256000000,6896432754839457130755425769163265163264000000
%N A382910 a(n) = A003266(n)^2.
%C A382910 For n>=3 number of valid symmetrical change ringing methods on n bells with the shortest number of rows per lead where the treble plain hunts out to the back. See Wikipedia and the Polster and Ross link for an explanation of bell ringing terminology.
%H A382910 Alois P. Heinz, <a href="/A382910/b382910.txt">Table of n, a(n) for n = 0..70</a>
%H A382910 Richard Duckworth and Fabian Stedman, <a href="https://www.gutenberg.org/files/18567/18567-h/18567-h.htm">Tintinnalogia, or, the Art of Ringing</a>, (1671). Released by Project Gutenberg, 2006.
%H A382910 Burkard Polster and Marty Ross, <a href="https://plus.maths.org/content/ringing-changes">Ringing the changes</a>, (2009).
%H A382910 Wikipedia, <a href="https://en.wikipedia.org/wiki/Method_ringing">Method ringing</a>.
%H A382910 <a href="/index/Be#bell_ringing">Index entries for sequences related to bell ringing</a>.
%F A382910 a(n) = Product_{j=1..n} Fibonacci(j)^2.
%F A382910 a(0) = 1; a(n) = a(n-1)*A007598(n). - _Hugo Pfoertner_, Apr 13 2025
%F A382910 a(n) ~ c^2 * phi^(n*(n+1)) / 5^n where phi is the golden ratio  (A001622) and c = A062073. - _Amiram Eldar_, Aug 18 2025
%p A382910 a:= proc(n) a(n):= `if`(n=0, 1, a(n-1)*(<<0|1>, <1|1>>^n)[1, 2]^2) end:
%p A382910 seq(a(n), n=0..16);  # _Alois P. Heinz_, Apr 14 2025
%t A382910 k = 1; {1, 1}~Join~Reap[Do[k *= Fibonacci[n]; Sow[k^2], {n, 16}] ][[-1, 1]] (* _Michael De Vlieger_, Apr 14 2025 *)
%Y A382910 Cf. A000045, A001622, A003266, A007598, A062073, A090281.
%K A382910 nonn,easy
%O A382910 0,4
%A A382910 _Edwin Hermann_, Apr 08 2025