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.

1, 21, 693, 23940, 734643, 13697019, -494620749, -83079255420, -6814815765975, -444980496382695, -25071954462140859, -1226361084729855984, -49426887403935395172, -1287188243957889124740, 23935850133162849385308, 6798920856226697943604944, 650950202721260061404073891

Offset

0,2

Links

Gheorghe Coserea, Table of n, a(n) for n = 0..201

Robert S. Maier, On Rationally Parametrized Modular Equations, arXiv:math/0611041 [math.NT], 2006.

Formula

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.

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).

Example

A(x) = 1 + 21*x + 693*x^2 + 23940*x^3 + ... is the g.f.

Mathematica

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;
Table[a[n], {n, 0, 16}] (* Jean-François Alcover, Oct 19 2018 *)

Prog

(PARI)
seq(N) = {
  my(a = vector(N)); a[1] = 21; a[2] = 693;
  for (n=3, N,
       a[n] = (3*(39*n^2 - 52*n + 20) * a[n-1] - 441*(3*n-4)^2 * a[n-2])/n^2);
  concat(1, a);
};
seq(17)
(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

Crossrefs

Cf. A091401, A276018.

Sequence in context: A212734 A339119 A243746 * A100713 A056565 A187359

Adjacent sequences: A276018 A276019 A276020 * A276022 A276023 A276024

Keyword

sign

Author

Gheorghe Coserea, Aug 23 2016

Status

approved