%I A051925
%S A051925 0,0,3,11,26,50,85,133,196,276,375,495,638,806,1001,1225,1480,1768,
%T A051925 2091,2451,2850,3290,3773,4301,4876,5500,6175,6903,7686,8526,9425,
%U A051925 10385,11408,12496,13651,14875,16170,17538,18981,20501,22100,23780
%N A051925 n(2n+5)(n-1)/6.
%C A051925 Related to variance of number of inversions of a random permutation of 
               n letters.
%C A051925 Zero followed by partial sums of A005563. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), 
               Oct 17 2008]
%C A051925 Definition: A051925=A000330-A000027 (square pyramidal numbers minus natural 
               numbers) [From Andrey Kostenko (Andrey.Kostenko(AT)buseco.monash.edu.au), 
               Nov 30 2008]
%D A051925 V. N. Sachkov, Probablistic Methods in Combinatorial Analysis, Cambridge, 
               1997.
%D A051925 J. Wang and H. Li, The upper bound of essential chromatic numbers of 
               hypergraphs, Discr. Math. 254 (2002), 555-564.
%p A051925 a:=n->sum((n+j^2),j=0..n): seq(a(n),n=-1..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 27 2006
%p A051925 seq(sum(k^2-1, k=1..n), n=0..41); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jan 28 2008
%p A051925 with(finance):seq(add(cashflows([n,k^2,0], 0 ), k=0..n), n=-1..45); # 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%t A051925 lst={0};s=0;Do[s+=n^2-1;AppendTo[lst, s], {n, 5!}];lst...and/or... lst={};
               Do[s=n*(2*n+5)*(n-1)/6;AppendTo[lst, s], {n, 0, 5!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Sep 30 2008]
%o A051925 (PARI) {print1(a=0, ","); for(n=0, 42, print1(a=a+(n+1)^2-1, ","))} [From 
               Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 17 2008]
%Y A051925 Sequence in context: A124078 A096795 A160039 this_sequence A011942 A101612 
               A123928
%Y A051925 Adjacent sequences: A051922 A051923 A051924 this_sequence A051926 A051927 
               A051928
%K A051925 nonn
%O A051925 0,3
%A A051925 N. J. A. Sloane (njas(AT)research.att.com), Dec 19 1999