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A235793 Sum of all parts of all overpartitions of n.

%I A235793 #17 May 19 2018 18:00:16
%S A235793 2,8,24,56,120,240,448,800,1386,2320,3784,6048,9464,14560,22080,32992,
%T A235793 48688,71064,102600,146720,207984,292336,407744,564672,776650,1061424,
%U A235793 1442016,1947904,2617192,3498720,4654464,6163584,8126448,10669472,13952400,18175896
%N A235793 Sum of all parts of all overpartitions of n.
%C A235793 The equivalent sequence for partitions is A066186.
%H A235793 Alois P. Heinz, <a href="/A235793/b235793.txt">Table of n, a(n) for n = 1..1000</a>
%F A235793 a(n) = n*A015128(n).
%F A235793 a(n) ~ exp(Pi*sqrt(n)) / 8. - _Vaclav Kotesovec_, May 19 2018
%p A235793 b:= proc(n, i) option remember; `if`(n=0, [1, 0],
%p A235793       `if`(i<1, [0$2], b(n, i-1)+add((l-> l+[0, l[1]*i*j])
%p A235793        (2*b(n-i*j, i-1)), j=1..n/i)))
%p A235793     end:
%p A235793 a:= n-> b(n$2)[2]:
%p A235793 seq(a(n), n=1..40);  # _Alois P. Heinz_, Jan 21 2014
%t A235793 Table[n*Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 1, 40}] (* _Jean-François Alcover_, Oct 20 2016, after _Vaclav Kotesovec_ *)
%Y A235793 Cf. A015128, A066186, A235790, A235792, A235797, A235798, A236000.
%K A235793 nonn
%O A235793 1,1
%A A235793 _Omar E. Pol_, Jan 18 2014