A019584 a(n) = n^2*(n-1)^3/4.
0, 0, 1, 18, 108, 400, 1125, 2646, 5488, 10368, 18225, 30250, 47916, 73008, 107653, 154350, 216000, 295936, 397953, 526338, 685900, 882000, 1120581, 1408198, 1752048, 2160000, 2640625, 3203226, 3857868, 4615408, 5487525, 6486750, 7626496, 8921088, 10385793
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..600
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Crossrefs
Cf. A099903.
Programs
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Magma
[n^2*(n-1)^3/4: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
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Mathematica
Table[n^2*(n-1)^3/4, {n,0,100}] -
PARI
a(n)=n^2*(n-1)^3/4 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = Sum_{j=1..n-2} Sum_{i=1..n-2} (i^3 + j^3)/2. - Alexander Adamchuk, Oct 24 2004
G.f.: x^2*(1 + 12*x + 15*x^2 + 2*x^3)/(1 - x)^6. - Colin Barker, May 04 2012
a(n) = Sum_{i=0..n-1} (n-1)*(n-1-i)^3 for n>0. - Bruno Berselli, Oct 31 2017
From Amiram Eldar, Feb 13 2023: (Start)
a(n) = A099903(n-1)/2.
Sum_{n>=2} 1/a(n) = 16 - 2*Pi^2 + 4*zeta(3).
Sum_{n>=2} (-1)^n/a(n) = 24*log(2) - 16 - Pi^2/3 + 3*zeta(3). (End)