Search: id:A066183
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%I A066183
%S A066183 1,6,17,44,87,180,311,558,910,1494,2302,3608,5343,7986,11554,16714,
%T A066183 23549,33270,45942,63506,86338,117156,156899,209926,277520,366260,
%U A066183 479012,624956,808935,1044994,1340364,1715572,2182935,2770942,3499379
%N A066183 Total sum of squares of parts in all partitions of n.
%C A066183 Sum of hook lengths of all boxes in the Ferrers diagrams of all partitions 
               of n (see the Guo-Niu Han paper, p. 25, Corollary 6.5). Example: 
               a(3)=17 because for the partitions (3), (2,1), (1,1,1) of n=3 the 
               hook length multi-sets are {3,2,1}, {3,1,1},{3,2,1}, respectively; 
               the total sum of all hook lengths is 6+5+6=17. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               May 15 2008
%D A066183 Guo-Niu Han, An explicit expansion formula for the powers of the Euler 
               product in terms of partition hook lengths, arXiv:0804.1849v3 [math.CO] 
               9 May 2008.
%F A066183 Sum_{k=1..n} sigma_2(k)*numbpart(n-k), where sigma_2(k)=sum of squares 
               of divisors of k=A001157(k). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Jan 26 2002
%e A066183 a(3)=17 because the squares of all partitions of 3 are {9},{4,1} and 
               {1,1,1}, summing to 17.
%t A066183 Table[Apply[Plus, Partitions[n]^2, {0, 2}], {n, 30}]
%Y A066183 Cf. A000041, A001157.
%Y A066183 Sequence in context: A047861 A099858 A062020 this_sequence A048746 A026382 
               A054492
%Y A066183 Adjacent sequences: A066180 A066181 A066182 this_sequence A066184 A066185 
               A066186
%K A066183 easy,nonn
%O A066183 1,2
%A A066183 Wouter Meeussen (wouter.meeussen(AT)pandora.be), Dec 15 2001
%E A066183 More terms from Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 07 2002

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