A026337 a(n) = 4^n*(4^n - 1)/2.

0, 6, 120, 2016, 32640, 523776, 8386560, 134209536, 2147450880, 34359607296, 549755289600, 8796090925056, 140737479966720, 2251799780130816, 36028796884746240, 576460751766552576, 9223372034707292160, 147573952581086478336, 2361183241400462868480

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (20,-64).

Crossrefs

Cf. A166984.

Programs

Magma

[4^n*(4^n-1)/2: n in [0..30]]; // Vincenzo Librandi, May 01 2011

Maple

seq(binomial(4^n,2),n=0..18); # Zerinvary Lajos, Jan 07 2008

Mathematica

Table[4^n (4^n-1)/2,{n,0,30}] (* or *) LinearRecurrence[{20,-64},{0,6},30] (* Harvey P. Dale, Nov 05 2023 *)

SageMath

[binomial(4^n, 2) for n in range(21)] # G. C. Greubel, Oct 02 2024

Formula

a(n) = binomial(4^n, 2), n >= 0. - Zerinvary Lajos, Jan 07 2008

From R. J. Mathar, Mar 20 2009: (Start)

a(n) = 20*a(n-1) - 64*a(n-2).

G.f.: 6*x/((1-4*x)*(1-16*x)). (End)

a(n) = 6*A166984(n-1). - R. J. Mathar, Jun 23 2013

E.g.f.: exp(10*x)*sinh(6*x). - G. C. Greubel, Oct 02 2024