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A276021 n^2 * a(n) = 3*(39*n^2 - 52*n + 20) * a(n-1) - 441*(3*n-4)^2 * a(n-2), with a(0)=1, a(1)=21.

%I A276021 #19 Sep 08 2022 08:46:17
%S A276021 1,21,693,23940,734643,13697019,-494620749,-83079255420,
%T A276021 -6814815765975,-444980496382695,-25071954462140859,
%U A276021 -1226361084729855984,-49426887403935395172,-1287188243957889124740,23935850133162849385308,6798920856226697943604944,650950202721260061404073891
%N A276021 n^2 * a(n) = 3*(39*n^2 - 52*n + 20) * a(n-1) - 441*(3*n-4)^2 * a(n-2), with a(0)=1, a(1)=21.
%H A276021 Gheorghe Coserea, <a href="/A276021/b276021.txt">Table of n, a(n) for n = 0..201</a>
%H A276021 Robert S. Maier, <a href="http://arxiv.org/abs/math/0611041">On Rationally Parametrized Modular Equations</a>, arXiv:math/0611041 [math.NT], 2006.
%F A276021 n^2 * a(n) = 3*(39*n^2-52*n+20) * a(n-1) - 441*(3*n-4)^2 * a(n-2), with a(0)=1, a(1)=21.
%F A276021 0 = 9*x*(x^2+13*x+49)*y'' + (21*x^2 + 195*x + 441)*y' + (4*x+21)*y, where y(x) = A(x/-441).
%e A276021 A(x) = 1 + 21*x + 693*x^2 + 23940*x^3 + ... is the g.f.
%t A276021 a[0] = 1; a[1] = 21; a[n_] := a[n] = (3(39n^2 - 52n + 20) a[n-1] - 441(3n - 4)^2 a[n-2])/n^2;
%t A276021 Table[a[n], {n, 0, 16}] (* _Jean-François Alcover_, Oct 19 2018 *)
%o A276021 (PARI)
%o A276021 seq(N) = {
%o A276021   my(a = vector(N)); a[1] = 21; a[2] = 693;
%o A276021   for (n=3, N,
%o A276021        a[n] = (3*(39*n^2 - 52*n + 20) * a[n-1] - 441*(3*n-4)^2 * a[n-2])/n^2);
%o A276021   concat(1,a);
%o A276021 };
%o A276021 seq(17)
%o A276021 (Magma) I:=[21,693]; [1] cat [n le 2 select I[n] else (3*(39*n^2-52*n+20)*Self(n-1)-441*(3*n-4)^2*Self(n-2)) div n^2: n in [1..30]]; // _Vincenzo Librandi_, Aug 25 2016
%Y A276021 Cf. A091401, A276018.
%K A276021 sign
%O A276021 0,2
%A A276021 _Gheorghe Coserea_, Aug 23 2016