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

1,1

Comments

The equivalent sequence for partitions is A066186.

Links

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

Formula

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

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

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 *)

Crossrefs

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

Sequence in context: A330520 A009059 A009297 * A182736 A083553 A051745

Adjacent sequences: A235790 A235791 A235792 * A235794 A235795 A235796

Keyword

nonn

Author

Omar E. Pol, Jan 18 2014

Status

approved