OFFSET
1,1
COMMENTS
It appears that a(n) is also the sum of largest parts of all overpartitions of n.
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.
The equivalent sequence for partitions is A006128.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Alois P. Heinz)
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]*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
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 18 2014
EXTENSIONS
More terms from Alois P. Heinz, Jan 21 2014
STATUS
approved