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(2*n+1)*(n+1)*(2*n^2+3*n-1).
1

%I #17 Jul 31 2015 20:39:05

%S -1,24,195,728,1935,4224,8099,14160,23103,35720,52899,75624,104975,

%T 142128,188355,245024,313599,395640,492803,606840,739599,893024,

%U 1069155,1270128,1498175,1755624,2044899,2368520,2729103,3129360,3572099,4060224,4596735,5184728,5827395,6528024

%N (2*n+1)*(n+1)*(2*n^2+3*n-1).

%D Fredrick T. Wall, Chemical Thermodynamics, W. H, Freeman, San Francisco, 1965, page 269

%H Harvey P. Dale, <a href="/A123197/b123197.txt">Table of n, a(n) for n = 0..1000</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)-a(n-1) = (4*n + 1)*(4*n^2 + 2*n - 1).

%F G.f.: (-1+29*x+65*x^2+3*x^3)/(1-x)^5. [Colin Barker, Jan 28 2012]

%F a(0)=-1, a(1)=24, a(2)=195, a(3)=728, a(4)=1935, a(n)=5*a(n-1)- 10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - _Harvey P. Dale_, May 29 2014

%t f[m_] = Sum[(4*n + 1)*(4*n^2 + 2*n - 1), {n, 0, m}]; a = Table[f[n], {n, 0, 50}]

%t Table[(2n+1)(n+1)(2n^2+3n-1),{n,0,40}] (* or *) LinearRecurrence[ {5,-10,10,-5,1},{-1,24,195,728,1935},40] (* _Harvey P. Dale_, May 29 2014 *)

%K sign,easy

%O 0,2

%A _Roger L. Bagula_, Oct 04 2006

%E Definition made precise by the Assoc. Eds. of the OEIS, Mar 27 2010