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%I #18 Sep 24 2023 11:10:13
%S 0,0,0,48,264,840,2040,4200,7728,13104,20880,31680,46200,65208,89544,
%T 120120,157920,204000,259488,325584,403560,494760,600600,722568,
%U 862224,1021200,1201200,1404000,1631448,1885464,2168040,2481240,2827200
%N a(n) = n*(n^2-1)*(3*n+2).
%D George E. Andrews, Number Theory, Dover Publications, New York, 1971, p. 4.
%H G. C. Greubel, <a href="/A115056/b115056.txt">Table of n, a(n) for n = 1..5000</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _G. C. Greubel_, Jul 17 2017: (Start)
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F G.f.: 24*x^2*(x+2)/(1-x)^5.
%F E.g.f.: (3*x^4 + 20*x^3 + 24*x^2)*exp(x). (End)
%F From _Amiram Eldar_, Mar 12 2023: (Start)
%F Sum_{n>=2} 1/a(n) = 27*log(3)/20 - 3*sqrt(3)*Pi/20 - 16/25.
%F Sum_{n>=2} (-1)^n/a(n) = 3*sqrt(3)*Pi/10 - 4*log(2)/5 - 53/50. (End)
%t Table[3*n^4 + 2*n^3 - 3*n^2 - 2*n, {n, -1, 50}] (* _G. C. Greubel_, Jul 17 2017 *)
%o (PARI) g(n) = for(x=0,n,y=x*(x^2-1)*(3*x+2);print1(y","))
%o (PARI) my(x='x+O('x^50)); concat([0,0,0], Vec(24*x^2*(x+2)/(1-x)^5)) \\ _G. C. Greubel_, Jul 17 2017
%K nonn,easy
%O -1,4
%A _Cino Hilliard_, Feb 28 2006
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