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%I #16 Mar 11 2014 01:34:20
%S 1,5,14,43,98,255,532,1201,2413,4968,9427,18475
%N Sum of all region numbers of all parts of all partitions of n.
%C Each part of a partition of n belongs to a different region of n. The "region number" of a part of the r-th region of n is equal to r. For the definition of "region of n" see A206437.
%H Omar E. Pol, <a href="http://www.polprimos.com/imagenespub/polpar02.jpg">Illustration of the seven regions of 5</a>
%e For n = 5 we have:
%e ---------------------------------------------------
%e . Two arrangements
%e k of the partitions of 5
%e ---------------------------------------------------
%e 7 [5] [5]
%e 6 [3+2] [3+2]
%e 5 [4+1] [4 +1]
%e 4 [2+1+1] [2+2 +1]
%e 3 [3+1+1] [3 +1 +1]
%e 2 [2+1+1+1] [2+1 +1 +1]
%e 1 [1+1+1+1+1] [1+1+1 +1 +1]
%e ---------------------------------------------------
%e . Two arrangements
%e . of the region numbers Sum of
%e k of the partitions of 5 zone k
%e ---------------------------------------------------
%e 7 [7] [7] 7
%e 6 [6,7] [6,7] 13
%e 5 [5,7] [5, 7] 12
%e 4 [4,5,7] [4,5, 7] 16
%e 3 [3,5,7] [3, 5, 7] 15
%e 2 [2,3,5,7] [2,3, 5, 7] 17
%e 1 [1,2,3,5,7] [1,2,3, 5, 7] 18
%e ---------------------------------------------------
%e The total sum is a(5) = 1+2^2+3^2+4+5^2+6+7^2 = 1+4+9+4+25+6+49 = 18+17+15+16+12+13+7 = 98.
%Y Partial sums of A210969. Row sums of triangle A210971.
%Y Cf. A135010, A138121, A182703, A194446, A210437, A210966.
%K nonn,more
%O 1,2
%A _Omar E. Pol_, Jun 30 2012
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