A235793 Sum of all parts of all overpartitions of n.

2, 8, 24, 56, 120, 240, 448, 800, 1386, 2320, 3784, 6048, 9464, 14560, 22080, 32992, 48688, 71064, 102600, 146720, 207984, 292336, 407744, 564672, 776650, 1061424, 1442016, 1947904, 2617192, 3498720, 4654464, 6163584, 8126448, 10669472, 13952400, 18175896

Offset: 1

Author

Omar E. Pol, Jan 18 2014

Keywords

• nonn

Comments

The equivalent sequence for partitions is A066186.

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A015128, A066186, A235790, A235792, A235797, A235798, A236000.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, [1, 0],
      `if`(i<1, [0$2], b(n, i-1)+add((l-> l+[0, l[1]*i*j])
       (2*b(n-i*j, i-1)), j=1..n/i)))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..40);  # Alois P. Heinz, Jan 21 2014

Mathematica

Table[n*Sum[PartitionsP[n-k]*PartitionsQ[k], {k, 0, n}], {n, 1, 40}] (* Jean-François Alcover, Oct 20 2016, after Vaclav Kotesovec *)

Formula

a(n) = n*A015128(n).

a(n) ~ exp(Pi*sqrt(n)) / 8. - Vaclav Kotesovec, May 19 2018