OFFSET
0,1
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's MathWorld, Polygamma Function.
Wikipedia, Polygamma Function.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Colin Barker, Mar 29 2017: (Start)
G.f.: (9 + x)*(1 + 4*x) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2.
(End)
Sum_{n>=0} 1/a(n) = polygamma(1, 3/5)/25. - Amiram Eldar, Oct 02 2020
EXAMPLE
a(0) = (5*0 + 3)^2 = 9.
MATHEMATICA
(5*Range[0, 40]+3)^2 (* or *) LinearRecurrence[{3, -3, 1}, {9, 64, 169}, 40] (* Harvey P. Dale, Dec 09 2016 *)
CoefficientList[Series[(9 + x) (1 + 4 x)/(1 - x)^3, {x, 0, 40}], x] (* Michael De Vlieger, Mar 29 2017 *)
PROG
(PARI) Vec((9 + x)*(1 + 4*x) / (1 - x)^3 + O(x^50)) \\ Colin Barker, Mar 29 2017
(Magma) [(5*n + 3)^2 : n in [0..50]]; // Wesley Ivan Hurt, Dec 02 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved