OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 2*A092364(n+1). - Zerinvary Lajos, May 09 2007
G.f.: -2*x*(4 + 7*x + x^2)/(x - 1)^5. - R. J. Mathar, Mar 10 2011
a(n) = A085537(n-1). - Eric W. Weisstein, Sep 08 2017
E.g.f.: exp(x)*x*(8 + 19*x + 9*x^2 + x^3). - Stefano Spezia, Jun 10 2023
From Amiram Eldar, Jul 02 2023: (Start)
Sum_{n>=1} 1/a(n) = 3 - Pi^2/6 - zeta(3).
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/12 + 2*log(2) + 3*zeta(3)/4 - 3. (End)
MATHEMATICA
Table[n (n + 1)^3, {n, 0, 40}] (* Vincenzo Librandi, Aug 15 2016 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 8, 54, 192, 500}, 40] (* Harvey P. Dale, May 06 2019 *)
PROG
(Magma) [n*(n+1)^3: n in [0..40]]; // Vincenzo Librandi, Aug 15 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 05 2003
STATUS
approved