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%I #21 Sep 08 2022 08:46:16
%S 0,1,24,171,704,2125,5256,11319,22016,39609,67000,107811,166464,
%T 248261,359464,507375,700416,948209,1261656,1653019,2136000,2725821,
%U 3439304,4294951,5313024,6515625,7926776,9572499,11480896,13682229,16209000,19096031,22380544,26102241
%N a(n) = n^3*(2*n^2+1)/3.
%C Partial sums are in A271535.
%C After 1, is A195279 the second bisection?
%H Vincenzo Librandi, <a href="/A272125/b272125.txt">Table of n, a(n) for n = 0..1000</a>
%H R. D. Carmichael and T. L. DeLand, <a href="http://www.jstor.org/stable/2967699">Find the sum of the series 1^2 + 5^2 + 14^2 + 30^2 + ... + [n*(n+1)*(2*n+1)/6]^2</a>, American Mathematical Monthly, Vol. 15, No. 6/7, Jun-Jul, 1908, pp. 132-133.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F O.g.f.: x*(1+18*x+42*x^2+18*x^3+x^4)/(1-x)^6.
%F E.g.f.: x*(3+33*x+51*x^2+20*x^3+2*x^4)*exp(x)/3.
%F 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).
%t Table[n^3 (2 n^2 + 1)/3, {n, 0, 40}]
%o (Magma) [n^3*(2*n^2+1)/3: n in [0..40]];
%o (PARI) vector(100, n, n--; n^3*(2*n^2+1)/3) \\ _Altug Alkan_, Apr 22 2016
%Y Cf. A271535.
%K nonn,easy
%O 0,3
%A _Vincenzo Librandi_, Apr 22 2016
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