A276177 n^2 * a(n) = 6*(66*n^2 - 94*n + 41) * a(n-1) - 36*(2016*n^2 - 5712*n + 4387) * a(n-2) + 50544*(132*n^2 - 560*n + 609) * a(n-3) - 7884864*(6*n-17)^2*a(n-4), with a(0)=1, a(1)=78, a(2)=4446, a(3)=20124.

1, 78, 4446, 20124, -38185290, -6138851004, -560711991060, -21068540562888, 3057536757534246, 744702083933794740, 85203074089262120004, 5052846560269468159368, -180318018879496001303748, -86176724948835065345458008, -11276003918572185562671306600, -751248675388448553292016521104

Offset: 0

Author

Gheorghe Coserea, Aug 23 2016

Keywords

• sign

Examples

			A(x) = 1 + 78*x + 4446*x^2 + 20124*x^3 + ... is the g.f.
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 0..301
• Robert S. Maier, On Rationally Parametrized Modular Equations, arXiv:math/0611041 [math.NT], 2006.

Crossrefs

Cf. A091401, A276018.

Programs

Magma

I:=[78,4446,20124,-38185290]; [1] cat [n le 4 select I[n] else (6*(66*n^2-94*n+41)*Self(n-1)-36*(2016*n^2-5712*n+4387)*Self(n-2)+50544*(132*n^2-560*n+ 609)*Self(n-3)-7884864*(6*n-17)^2*Self(n-4)) div n^2: n in [1..30]]; // Vincenzo Librandi, Aug 25 2016

Mathematica

a[0] = 1; a[1] = 78; a[2] = 4446; a[3] = 20124; a[n_] := a[n] = (6(66n^2 - 94n + 41) a[n-1] - 36(2016n^2 - 5712n + 4387)a[n-2] + 50544(132n^2 - 560n + 609)a[n-3] - 7884864(6n - 17)^2 a[n-4])/n^2;
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, Oct 19 2018 *)

PARI

seq(N) = {
  my(a = vector(N));
  a[1] = 78; a[2] = 4446; a[3] = 20124; a[4] = -38185290;
  for (n = 5, N,
       my(t1 = 6*(66*n^2 - 94*n + 41) * a[n-1],
          t2 = -36*(2016*n^2 - 5712*n + 4387) * a[n-2],
          t3 = 50544*(132*n^2 - 560*n + 609) * a[n-3],
          t4 = -7884864*(6*n-17)^2 * a[n-4]);
       a[n] = (t1 + t2 + t3 + t4)/n^2);
  concat(1,a);
};
seq(17)

Formula

n^2 * a(n) = 6*(66*n^2 - 94*n + 41) * a(n-1) - 36*(2016*n^2 - 5712*n + 4387) * a(n-2) + 50544*(132*n^2 - 560*n + 609) * a(n-3) - 7884864*(6*n-17)^2*a(n-4), with a(0)=1, a(1)=78, a(2)=4446, a(3)=20124.

0 = 36*x*(x^2 + 5*x + 13)*(x^2 + 6*x + 13)*y'' + 12*(10*x^4 + 91*x^3 + 364*x^2 + 676*x + 507)*y' + (49*x^3 + 351*x^2 + 1027*x + 1014)*y, where y(x) = A(x/-468).