%I #28 Jul 06 2019 02:59:30
%S 0,2,3,8,10,24,28,56,72,120,154,252,312,476,615,880,1122,1584,1995,
%T 2740,3465,4620,5819,7680,9575,12428,15498,19824,24563,31170,38378,
%U 48224,59202,73678,90055,111384,135420,166364,201630,246120,297045,360822
%N Sum of all parts of all partitions of n that do not contain 1 as a part.
%C Sum of all parts > 1 of the last section of the set of partitions of n.
%C Row sums of triangle A182710. Also row sums of other similar triangles as A138136 and A182711.
%C Partial sums give A194552. - _Omar E. Pol_, Sep 23 2013
%H Vaclav Kotesovec, <a href="/A138880/b138880.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A002865(n)*n = (A000041(n) - A000041(n-1))*n = A138879(n) - A000041(n-1).
%F a(n) ~ Pi^2/6*A000070(n-2). - _Peter Bala_, Dec 23 2013
%F G.f.: x*f'(x), where f(x) = Product_{k>=2} 1/(1 - x^k). - _Ilya Gutkovskiy_, Apr 13 2017
%F a(n) ~ Pi * exp(sqrt(2*n/3)*Pi) / (12*sqrt(2*n)) * (1 - (3*sqrt(3/2)/Pi + 13*Pi/(24*sqrt(6)))/sqrt(n) + (217*Pi^2/6912 + 9/(2*Pi^2) + 13/8)/n). - _Vaclav Kotesovec_, Jul 06 2019
%t Table[Total[Flatten[Select[IntegerPartitions[n],FreeQ[#,1]&]]],{n,50}] (* _Harvey P. Dale_, May 24 2015 *)
%t a[n_] := (PartitionsP[n] - PartitionsP[n-1])*n; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Oct 07 2015 *)
%Y Cf. A000041, A002865, A066186, A133041, A138135, A138136, A138137, A138138, A138151, A138879, A139100.
%K nonn
%O 1,2
%A _Omar E. Pol_, Apr 30 2008
%E Better definition from _Omar E. Pol_, Sep 23 2013