A276020 - OEIS

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.

1, 10, 90, 780, 6630, 55820, 469220, 3967000, 33951750, 295553500, 2622492940, 23701797800, 217528135900, 2018704327800, 18862262001800, 176834576018480, 1659586559786950, 15575074941839100, 146164364053448700, 1372547571923176200, 12910383388613518580, 121770360957324308200, 1152648798132152849400

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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) = 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.

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).

a(n) ~ 2^n * 5^(n+5/4) / (Pi*n). - Vaclav Kotesovec, Aug 25 2016

MATHEMATICA

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;

Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Oct 19 2018 *)

PROG

(PARI)

seq(N) = {

my(a = vector(N));

a[1] = 10; a[2] = 90; a[3] = 780; a[4] = 6630;

for (n = 5, N,

my(t1 = 2*(17*n^2 - 21*n + 9)*a[n-1] - 4*(112*n^2 - 280*n + 197)*a[n-2],

t2 = 40*(68*n^2 - 256*n + 251) * a[n-3] - 1600*(2*n-5)^2 *a[n-4]);

a[n] = (t1 + t2)/n^2);

concat(1, a);

};