OFFSET
1,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 1000 terms from Seiichi Manyama)
Arnold Knopfmacher and Neville Robbins, Identities for the total number of parts in partitions of integers, Util. Math. 67 (2005), 9-18.
FORMULA
G.f.: Sum_{n>=1} (2*n-1)*x^(2*n-1)*Product_{k=1..n-1} (1+x^(2*k-1)).
EXAMPLE
a(13) = 29 because the partitions of 13 into distinct odd parts are [13],[9,3,1] and [7,5,1], with sum of largest terms 13+9+7 = 29.
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1 or i^2<n,
0, b(n, i-1)+ (t-> `if`(t>n, 0, b(n-t, i-1)))(2*i-1) ))
end:
a:= n-> add(`if`(j::odd, j*b(n-j, (j-1)/2), 0), j=1..n):
seq(a(n), n=1..55); # Alois P. Heinz, Jan 19 2022
MATHEMATICA
nmax = 50; Rest[CoefficientList[Series[Sum[(2*k - 1)*x^(2*k - 1) * Product[1 + x^(2*j - 1), {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, Jun 28 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 15 2004
EXTENSIONS
More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004
STATUS
approved