OFFSET
0,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
Euler transform of {Q(1), 0, Q(3), 0, Q(5), 0, ...} where Q = A000009.
EXAMPLE
The a(6) = 9 multiset partitions using odd-weight strict partitions: (5)(1), (14)(1), (3)(3), (32)(1), (3)(21), (3)(1)(1)(1), (21)(21), (21)(1)(1)(1), (1)(1)(1)(1)(1)(1).
The a(6) = 9 multiset partitions using odd partitions: (5)(1), (3)(3), (311)(1), (3)(111), (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(b(n-j)*add(
`if`(d::odd, d, 0), d=divisors(j)), j=1..n)/n)
end:
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
`if`(d::odd, b(d)*d, 0), d=divisors(j)), j=1..n)/n)
end:
seq(a(n), n=0..45); # Alois P. Heinz, Mar 02 2018
MATHEMATICA
nn=50;
ser=Product[1/(1-x^n)^PartitionsQ[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