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A016886 a(n) = (5*n + 3)^2. 3
9, 64, 169, 324, 529, 784, 1089, 1444, 1849, 2304, 2809, 3364, 3969, 4624, 5329, 6084, 6889, 7744, 8649, 9604, 10609, 11664, 12769, 13924, 15129, 16384, 17689, 19044, 20449, 21904, 23409, 24964, 26569, 28224, 29929, 31684, 33489, 35344, 37249, 39204, 41209 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
Eric Weisstein's MathWorld, Polygamma Function.
Wikipedia, Polygamma Function.
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)
a(n) = A000290(A016885(n)). - Michel Marcus, Mar 30 2017
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
Sequence in context: A165447 A050792 A171671 * A099761 A018201 A181888
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified April 18 11:52 EDT 2024. Contains 371779 sequences. (Running on oeis4.)