%I #24 May 24 2018 05:56:49

%S 2,6,16,34,68,128,228,390,650,1052,1664,2584,3940,5916,8768,12826,

%T 18552,26566,37672,52956,73848,102192,140420,191688,260038,350700,

%U 470384,627604,833236,1101080,1448500,1897438,2475464,3217016,4165200,5373714,6909180,8854288

%N Total number of parts in all overpartitions of n.

%C It appears that a(n) is also the sum of largest parts of all overpartitions of n.

%C More generally, It appears that the total number of parts >= k in all overpartitions of n equals the sum of k-th largest parts of all overpartitions of n. In this case k = 1. Also the first column of A235797.

%C The equivalent sequence for partitions is A006128.

%H Vaclav Kotesovec, <a href="/A235792/b235792.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Alois P. Heinz)

%p b:= proc(n, i) option remember; `if`(n=0, [1, 0],

%p `if`(i<1, [0$2], b(n, i-1)+add((l-> l+[0, l[1]*j])

%p (2*b(n-i*j, i-1)), j=1..n/i)))

%p end:

%p a:= n-> b(n$2)[2]:

%p seq(a(n), n=1..40); # _Alois P. Heinz_, Jan 21 2014

%t b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i<1, {0, 0}, b[n, i-1] + Sum[ Function[l, l+{0, l[[1]]*j}][2*b[n-i*j, i-1]], {j, 1, n/i}]]]; a[n_] := b[n, n][[2]]; Table[a[n], {n, 1, 40}] (* _Jean-François Alcover_, Nov 11 2015, after _Alois P. Heinz_ *)

%Y Cf. A006128, A015128, A211971, A235790, A235793, A235797, A235798, A236000, A236001.

%K nonn

%O 1,1

%A _Omar E. Pol_, Jan 18 2014

%E More terms from _Alois P. Heinz_, Jan 21 2014