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%I #19 Sep 08 2022 08:45:06
%S 0,0,4,23,76,190,400,749,1288,2076,3180,4675,6644,9178,12376,16345,
%T 21200,27064,34068,42351,52060,63350,76384,91333,108376,127700,149500,
%U 173979,201348,231826,265640,303025,344224,389488,439076,493255,552300,616494
%N a(n) = n*(n - 1)*(2*n^2 + n + 2)/6.
%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="/A071246/b071246.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5), n > 4, a(0)=0, a(1)=0, a(2)=4, a(3)=23, a(4)=76. [_Yosu Yurramendi_, Sep 03 2013]
%F From _Indranil Ghosh_, Apr 05 2017: (Start)
%F G.f.: -(4x^2 + 3x^3 + x^4)/(x - 1)^5.
%F E.g.f.: exp(x)*(x^2)*(12 + 11x + 2x^2)/6.
%F (End)
%t CoefficientList[Series[-(4x^2 + 3x^3 + x^4)/(x - 1)^5, {x, 0, 50}], x] (* or *) Table[n*(n - 1)*(2*n^2 + n + 2)/6, {n, 0, 50}] (* _Indranil Ghosh_, Apr 05 2017 *)
%o (Magma) [n*(n-1)*(2*n^2+n+2)/6: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o (PARI) a(n) = n*(n - 1)*(2*n^2 + n + 2)/6; \\ _Indranil Ghosh_, Apr 05 2017
%o (Python) def a(n): return n*(n - 1)*(2*n**2 + n + 2)/6 # _Indranil Ghosh_, Apr 05 2017
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Jun 12 2002
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