A016853 a(n) = (5*n)^5.

0, 3125, 100000, 759375, 3200000, 9765625, 24300000, 52521875, 102400000, 184528125, 312500000, 503284375, 777600000, 1160290625, 1680700000, 2373046875, 3276800000, 4437053125, 5904900000, 7737809375, 10000000000, 12762815625, 16105100000, 20113571875, 24883200000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

a(n) = A155955(n,5) for n > 4. - Reinhard Zumkeller, Jan 31 2009

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A000584.

Programs

Mathematica

(5 Range[0, 20])^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3125, 100000, 759375, 3200000, 9765625}, 20] (* Harvey P. Dale, Jul 11 2015 *)
CoefficientList[Series[3125 x (1 + 26 x + 66 x^2 + 26 x^3 + x^4) / (1-x)^6, {x, 0, 33}], x] (* Vincenzo Librandi, Oct 24 2017 *)

Formula

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), with a(0) = 0, a(1) = 3125, a(2) = 100000, a(3) = 759375, a(4) = 3200000, a(5) = 9765625. - Harvey P. Dale, Jul 11 2015

a(n) = 3125*A000584(n). - Michel Marcus, Oct 24 2017

G.f.: 3125*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^6. - Vincenzo Librandi, Oct 24 2017