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A071252 a(n) = n*(n - 1)*(n^2 + 1)/2.

%I A071252 #38 Aug 07 2024 02:25:02
%S A071252 0,0,5,30,102,260,555,1050,1820,2952,4545,6710,9570,13260,17927,23730,
%T A071252 30840,39440,49725,61902,76190,92820,112035,134090,159252,187800,
%U A071252 220025,256230,296730,341852,391935,447330,508400,575520,649077,729470,817110,912420
%N A071252 a(n) = n*(n - 1)*(n^2 + 1)/2.
%D A071252 T. A. Gulliver, Sequences from Arrays of Integers, Int. Math. Journal, Vol. 1, No. 4, pp. 323-332, 2002.
%H A071252 Vincenzo Librandi, <a href="/A071252/b071252.txt">Table of n, a(n) for n = 0..2000</a>
%H A071252 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A071252 a(n) = floor(n^5/(n+1))/2. - _Gary Detlefs_, Mar 31 2011
%F A071252 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)=5, a(3)=30, a(4)=102. - _Yosu Yurramendi_, Sep 03 2013
%F A071252 G.f.:  x^2*(5+5*x+2*x^2)/(1-x)^5. - _Joerg Arndt_, Sep 04 2013
%F A071252 From _Indranil Ghosh_, Apr 05 2017: (Start)
%F A071252 a(n) = A002378(n) * A002522(n) / 2.
%F A071252 E.g.f.: exp(x)*x^2*(5 + 5*x + x^2)/2.
%F A071252 (End)
%t A071252 f[n_] := n (n - 1) (n^2 + 1)/2 (* Or *) f[n_] := Floor[n^5/(n + 1)]/2; Array[f, 38, 0] (* _Robert G. Wilson v_, Apr 01 2012 *)
%o A071252 (Magma) [n*(n-1)*(n^2+1)/2: n in [0..40]]; // _Vincenzo Librandi_, Jun 14 2011
%o A071252 (PARI) a(n)=n*(n-1)*(n^2+1)/2; \\ _Joerg Arndt_, Sep 04 2013
%o A071252 (Python) def a(n): return  n*(n - 1)*(n**2 + 1)/2 # _Indranil Ghosh_, Apr 05 2017
%o A071252 (SageMath)
%o A071252 def A071252(n): return binomial(n,2)*(1+n^2)
%o A071252 [A071252(n) for n in range(41)] # _G. C. Greubel_, Aug 07 2024
%Y A071252 Cf. A002378, A002522, A071239, A071244, A071245, A071246.
%K A071252 nonn,easy
%O A071252 0,3
%A A071252 _N. J. A. Sloane_, Jun 12 2002