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%I #27 Sep 08 2022 08:46:16
%S 0,4,68,282,736,1520,2724,4438,6752,9756,13540,18194,23808,30472,
%T 38276,47310,57664,69428,82692,97546,114080,132384,152548,174662,
%U 198816,225100,253604,284418,317632,353336,391620,432574,476288,522852,572356,624890,680544
%N a(n) = n*(15*n^2 - 15*n + 4).
%H Vincenzo Librandi, <a href="/A272134/b272134.txt">Table of n, a(n) for n = 0..1000</a>
%H Richard P. Brent, <a href="http://arxiv.org/abs/1407.3533">Generalising Tuenter's binomial sums</a>, arXiv:1407.3533 [math.CO], 2014. (page 16)
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F O.g.f.: 2*x*(2 + 26*x + 17*x^2)/(1-x)^4.
%F E.g.f.: x*(4 + 30*x + 15*x^2)*exp(x).
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), for n>3.
%F See page 7 in Brent's paper:
%F a(n) = 2*n^2*A049450(n) - n*(2*n-1)*A049450(n-1).
%F A272357(n) = 2*n^2*a(n) - n*(2*n-1)*a(n-1).
%t Table[n (15 n^2 - 15 n + 4), {n, 0, 40}]
%o (Magma) [n*(15*n^2-15*n+4): n in [0..40]];
%o (PARI) vector(100, n, n--; n*(15*n^2 - 15*n + 4)) \\ _Altug Alkan_, Apr 28 2016
%o (Python) for n in range(0,10**3):print(n*(15*n**2-15*n+4),end=", ") # _Soumil Mandal_, Apr 30 2016
%Y Cf. A049450, A272357.
%K nonn,easy
%O 0,2
%A _Vincenzo Librandi_, Apr 27 2016
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