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A276020 n^2 * a(n) = 2*(17*n^2-21*n+9) * a(n-1) - 4*(112*n^2-280*n+197) * a(n-2) + 40*(68*n^2-256*n+251) * a(n-3) - 1600*(2*n-5)^2 * a(n-4), with a(0)=1, a(1)=10, a(2)=90, a(3)=780.

%I A276020 #14 Oct 19 2018 03:26:08
%S A276020 1,10,90,780,6630,55820,469220,3967000,33951750,295553500,2622492940,
%T A276020 23701797800,217528135900,2018704327800,18862262001800,
%U A276020 176834576018480,1659586559786950,15575074941839100,146164364053448700,1372547571923176200,12910383388613518580,121770360957324308200,1152648798132152849400
%N A276020 n^2 * a(n) = 2*(17*n^2-21*n+9) * a(n-1) - 4*(112*n^2-280*n+197) * a(n-2) + 40*(68*n^2-256*n+251) * a(n-3) - 1600*(2*n-5)^2 * a(n-4), with a(0)=1, a(1)=10, a(2)=90, a(3)=780.
%H A276020 Gheorghe Coserea, <a href="/A276020/b276020.txt">Table of n, a(n) for n = 0..201</a>
%H A276020 Robert S. Maier, <a href="http://arxiv.org/abs/math/0611041">On Rationally Parametrized Modular Equations</a>, arXiv:math/0611041 [math.NT], 2006.
%F A276020 n^2*a(n) = 2*(17*n^2-21*n+9)*a(n-1) - 4*(112*n^2-280*n+197)*a(n-2) + 40*(68*n^2-256*n+251)*a(n-3) - 1600*(2*n-5)^2 *a(n-4), with a(0)=1, a(1)=10, a(2)=90, a(3)=780.
%F A276020 0 = 4*x*(x+4)*(x+5)*(x^2+8*x+20)*y'' + 4*(4*x^4+55*x^3+280*x^2+600*x+400)*y' + (9*x^3+95*x^2+340*x+400)*y, where y(x) = A(x/-40).
%F A276020 a(n) ~ 2^n * 5^(n+5/4) / (Pi*n). - _Vaclav Kotesovec_, Aug 25 2016
%t A276020 a[0] = 1; a[1] = 10; a[2] = 90; a[3] = 780; a[n_] := a[n] = (40(68n^2 - 256n + 251)a[n-3] - 4(112n^2 - 280n + 197)a[n-2] + 2(17n^2 - 21n + 9)a[n-1] - 1600(2n - 5)^2 a[n-4])/n^2;
%t A276020 Table[a[n], {n, 0, 22}] (* _Jean-François Alcover_, Oct 19 2018 *)
%o A276020 (PARI)
%o A276020 seq(N) = {
%o A276020   my(a = vector(N));
%o A276020   a[1] = 10; a[2] = 90; a[3] = 780; a[4] = 6630;
%o A276020   for (n = 5, N,
%o A276020     my(t1 = 2*(17*n^2 - 21*n + 9)*a[n-1] - 4*(112*n^2 - 280*n + 197)*a[n-2],
%o A276020        t2 = 40*(68*n^2 - 256*n + 251) * a[n-3] - 1600*(2*n-5)^2 *a[n-4]);
%o A276020     a[n] = (t1 + t2)/n^2);
%o A276020   concat(1,a);
%o A276020 };
%o A276020 seq(22)
%Y A276020 Cf. A091401, A276018.
%K A276020 nonn
%O A276020 0,2
%A A276020 _Gheorghe Coserea_, Aug 23 2016