%I A101102
%S A101102 1,13,82,354,1200,3432,8646,19734,41613,82225,153868,274924,472056,
%T A101102 782952,1259700,1972884,3016497,4513773,6624046,9550750,13550680,
%U A101102 18944640,26129610,35592570,47926125,63846081,84211128,110044792
%N A101102 Fifth partial sums of cubes (A000578).
%H A101102 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, 
               Explorations and Formulas of the Euler/Pascal Cube</a>.
%F A101102 a(n) = {(n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(5 + n)*(10 + 3*n*(5 + n)))/
               20160}.
%F A101102 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=5 - Alexander R. 
               Povolotsky (pevnev(AT)juno.com), May 17 2008
%t A101102 s1=s2=s3=s4=s5=0; lst={}; Do[s1+=n^3; s2+=s1; s3+=s2; s4+=s3; s5+=s4; 
               AppendTo[lst,s5],{n,0,6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%o A101102 (PARI) a(n)=sum(t=1,n,sum(s=1,t,sum(l=1,s,sum(j=1,l, sum(m=1, j, sum(i=m*(m+1)/
               2-m+1, m*(m+1)/2,(2*i-1))))))) - Alexander R. Povolotsky (pevnev(AT)juno.com), 
               May 17 2008
%Y A101102 Cf. A101097.
%Y A101102 Cf. A101097, A101094, A024166, A000537.
%Y A101102 Cf. A024166, A101094, A101097 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%Y A101102 Sequence in context: A133718 A052255 A082203 this_sequence A142085 A163688 
               A010025
%Y A101102 Adjacent sequences: A101099 A101100 A101101 this_sequence A101103 A101104 
               A101105
%K A101102 easy,nonn
%O A101102 1,2
%A A101102 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
%E A101102 Edited by Ralf Stephan, Dec 16 2004