OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..5000
FORMULA
O.g.f.: Product_{n odd} 1/(1 - A000009(n)x^n).
EXAMPLE
The a(6) = 10 twice-partitions using odd partitions: (5)(1), (3)(3), (113)(1), (3)(111), (111)(3), (3)(1)(1)(1), (11111)(1), (111)(111), (111)(1)(1)(1), (1)(1)(1)(1)(1)(1).
MAPLE
with(numtheory):
b:= proc(n) option remember; `if`(n=0, 1, add(add(
`if`(d::odd, d, 0), d=divisors(j))*b(n-j), j=1..n)/n)
end:
g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
g(n, i-2)+`if`(i>n, 0, b(i)*g(n-i, i)))
end:
a:= n-> g(n, n-1+irem(n, 2)):
seq(a(n), n=0..50); # Alois P. Heinz, Mar 05 2018
MATHEMATICA
nn=50;
ser=Product[1/(1-PartitionsQ[n]x^n), {n, 1, nn, 2}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 02 2018
STATUS
approved