OFFSET
0,2
COMMENTS
An odd partition is an integer partition of an odd number with an odd number of parts, all of which are odd.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..4919
Gus Wiseman, "Twice-odd partitions of n=9."
EXAMPLE
The a(3)=15 ways to choose an odd partition of each part of an odd partition of 7 are:
((7)), ((511)), ((331)), ((31111)), ((1111111)), ((5)(1)(1)), ((311)(1)(1)),
((11111)(1)(1)), ((3)(3)(1)), ((3)(111)(1)), ((111)(3)(1)), ((111)(111)(1)),
((3)(1)(1)(1)(1)), ((111)(1)(1)(1)(1)), ((1)(1)(1)(1)(1)(1)(1)).
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(add(d*
[0, 2, 0, 1$4, 2, 0, 2, 1$4, 0, 2][1+irem(d, 16)],
d=numtheory[divisors](j))*g(n-j), j=1..n)/n)
end:
b:= proc(n, i, t) option remember;
`if`(n=0, t, `if`(i<1, 0, b(n, i-2, t)+
`if`(i>n, 0, b(n-i, i, 1-t)*g((i-1)/2))))
end:
a:= n-> b(2*n+1$2, 0):
seq(a(n), n=0..35); # Alois P. Heinz, Dec 12 2016
MATHEMATICA
nn=20; Table[SeriesCoefficient[Product[1/(1-PartitionsQ[k]x^k), {k, 1, 2n-1, 2}], {x, 0, 2n-1}], {n, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 11 2016
STATUS
approved