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%I #26 Oct 02 2023 20:10:27
%S 24,96,216,480,840,1584,2520,4224,6480,10080,14784,22176,31512,45360,
%T 63360,88704,121176,166320,223440,300960,399168,529056,692760,907200,
%U 1174800,1520064,1950480,2498496,3177240,4034880,5090448,6412032
%N a(n) = 24*n*p(n) = 24*n*A000041(n).
%C a(n) is also the sum of the partition number of n and the "trace" Tr(n) of A183011. a(n) = p(n) + Tr(n).
%C a(n) is also the number of "sectors" or "half-periods" in all partitions of n in some versions of the shell model of partitions of A135010.
%F a(n) = A008606(n)*A000041(n) = 24*A066186(n) = n*A183008(n).
%F a(n) = p(n) + Tr(n) = A000041(n) + A183011(n).
%F a(n) = 12*M_2(n) = 24*spt(n) + 12*N_2(n) = 12*A220909(n) = 24*A092269(n) + 12*A220908(n). - _Omar E. Pol_, Feb 17 2013
%e The number of partitions of 6 is p(6) = A000041(6) = 11, so a(6) = 24*6*11 = 1584.
%e Also the trace Tr(6) = A183011(6) = 1573, so a(6) = p(6) + Tr(6) = 11 + 1573 = 1584.
%t Table[24n*PartitionsP[n],{n,40}] (* _Harvey P. Dale_, Mar 07 2019 *)
%Y Partial sums of A183006. Column 24 of A182728.
%Y Cf. A000041, A000796, A008606, A018253, A066186, A135010, A182742, A182743, A183008, A183010, A183011.
%K nonn,easy
%O 1,1
%A _Omar E. Pol_, Jan 22 2011
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