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%I #53 Mar 29 2024 02:15:02
%S 0,0,3,19,66,170,365,693,1204,1956,3015,4455,6358,8814,11921,15785,
%T 20520,26248,33099,41211,50730,61810,74613,89309,106076,125100,146575,
%U 170703,197694,227766,261145,298065,338768,383504,432531,486115,544530,608058
%N a(n) = n*(n-1)*(2*n^2+1)/6.
%C The first differences are given in A277228. - _J. M. Bergot_, Sep 14 2016
%D T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H Vincenzo Librandi, <a href="/A071245/b071245.txt">Table of n, a(n) for n = 0..2000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 4; a(0)=0, a(1)=0, a(2)=3, a(3)=19, a(4)=66. - _Yosu Yurramendi_, Sep 03 2013
%F G.f.: (-3*x^2 - 4*x^3 - x^4)/(-1 + x)^5. - _Michael De Vlieger_, Sep 14 2016
%F E.g.f.: (1/6)*x^2*(9 + 10*x + 2*x^2)*exp(x). - _G. C. Greubel_, Sep 23 2016
%t Table[n (n - 1) (2 n^2 + 1)/6, {n, 0, 37}] (* or *)
%t CoefficientList[Series[(-3 x^2 - 4 x^3 - x^4)/(-1 + x)^5, {x, 0, 37}], x] (* _Michael De Vlieger_, Sep 14 2016 *)
%o (Magma) [n*(n-1)*(2*n^2+1)/6: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o (PARI) a(n)=n*(n-1)*(2*n^2+1)/6; \\ _Joerg Arndt_, Sep 04 2013
%Y Cf. A071238, A277228 (first differences).
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 12 2002
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