OFFSET
0,2
LINKS
Delbert L. Johnson, Table of n, a(n) for n = 0..19999
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
From Harvey P. Dale, May 26 2015: (Start)
G.f.: (3*x+14*x^2+3*x^3)/(x-1)^6.
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); a(0)=0, a(1)=3, a(2)=32, a(3)=150, a(4)=480, a(5)=1225. (End)
From Amiram Eldar, Nov 02 2021: (Start)
Sum_{n>=1} 1/a(n) = 3/8.
Sum_{n>=1} (-1)^(n+1)/a(n) = 69/8 - 12*log(2). (End)
MATHEMATICA
Table[(n^2 (n+1)(n+2)^2)/6, {n, 0, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {0, 3, 32, 150, 480, 1225}, 40] (* Harvey P. Dale, May 26 2015 *)
PROG
(Magma) [n^2*(n+1)*(n+2)^2/6 : n in [0..50]]; // Wesley Ivan Hurt, Jan 22 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved