A276019 n^2 * a(n) = (88*n^2 - 132*n + 54) * a(n-1) - 500*(2*n-3)^2 * a(n-2), with a(0)=1, a(1)=10.

1, 10, 230, 6500, 199750, 6366060, 204990300, 6539387400, 202432551750, 5897526329500, 151804596385780, 2807347223915000, -15232296765302500, -5584390420089725000, -416025902106681525000, -24002385182809425846000, -1235898175219724085176250, -59486502796252242452122500, -2731496764897242177292037500, -120874274801920384164027025000, -5181210157044172846922944311500

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) = (88*n^2-132*n+54)*a(n-1) - 500*(2*n-3)^2*a(n-2), with a(0)=1, a(1)=10.

0 = 4*x*(x^2+22*x+125)*y'' + (8*x^2+132*x+500)*y' + (x+10)*y, where y(x) = A(x/-500).

Example

A(x) = 1 + 10*x + 230*x^2 + 6500*x^3 + ... is the g.f.

Prog

(PARI)
seq(N) = {
  a = vector(N); a[1] = 10; a[2] = 230;
  for (n = 3, N, a[n] = ((88*n^2 - 132*n + 54)*a[n-1] - 500*(2*n-3)^2 * a[n-2])/n^2);
  concat(1, a);
};
seq(20)

Crossrefs

Cf. A091401, A276018.

Sequence in context: A211079 A211084 A302095 * A004702 A027952 A056602

Adjacent sequences: A276016 A276017 A276018 * A276020 A276021 A276022

Keyword

sign

Author

Gheorghe Coserea, Aug 23 2016

Status

approved