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 A101097 n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840. 8

%I

%S 1,12,69,272,846,2232,5214,11088,21879,40612,71643,121056,197132,

%T 310896,476748,713184,1043613,1497276,2110273,2926704,3999930,5393960,

%U 7184970,9462960,12333555,15919956,20365047,25833664,32515032,40625376,50410712

%N n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840.

%C Fourth partial sums of cubes (A000578).

%H C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, Explorations and Formulas of the Euler/Pascal Cube</a>.

%F This sequence could be obtained from the general formula a(n)=n*(n+1)*(n+2)*(n+3)* ...* (n+k) *(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=4 - _Alexander R. Povolotsky_, May 17 2008

%F O.g.f.: x(1+4x+x^2)/(1-x)^8. - R. J. Mathar, Jun 13 2008

%t s1=s2=s3=s4=0; lst={}; Do[s1+=n^3; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst,s4],{n,0,6!}]; lst [From _Vladimir Joseph Stephan Orlovsky_, Jan 15 2009]

%o (PARI) {A101097(n) =

%o n*(n+1)*(n+2)*(n+3)*(n+4)*(2+4*n+n^2)/840

%o } /* R. J. Mathar, Dec 06 2011 */

%Y Cf. A101102, A101094, A024166, A000537.

%K easy,nonn

%O 1,2

%A Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004

%E Edited by Ralf Stephan, Dec 16 2004

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