A016745 a(n) = (2*n)^5.

0, 32, 1024, 7776, 32768, 100000, 248832, 537824, 1048576, 1889568, 3200000, 5153632, 7962624, 11881376, 17210368, 24300000, 33554432, 45435424, 60466176, 79235168, 102400000, 130691232, 164916224, 205962976, 254803968, 312500000, 380204032, 459165024, 550731776

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A016757.

Programs

Magma

[(2*n)^5: n in [0..30]]; // Vincenzo Librandi, Sep 05 2011

Maple

A016745:=n->(2*n)^5: seq(A016745(n), n=0..50); # Wesley Ivan Hurt, Sep 15 2018

Mathematica

Table[(2*n)^5, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{0,32,1024,7776,32768,100000},30] (* Harvey P. Dale, Sep 15 2019 *)

PARI

vector(30, n, n--; (2*n)^5) \\ G. C. Greubel, Sep 15 2018

Formula

G.f.: 32*x*(1 + 26*x + 66*x^2 + 26*x^3 + x^4)/(1-x)^6. - Colin Barker, Sep 17 2012

E.g.f.: 32*x*(1 + 15*x + 25*x^2 + 10*x^3 + x^4)*exp(x). - G. C. Greubel, Sep 15 2018

From Amiram Eldar, Oct 10 2020: (Start)

Sum_{n>=1} 1/a(n) = zeta(5)/32.

Sum_{n>=1} (-1)^(n+1)/a(n) = 15*zeta(5)/512. (End)