OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..4000
EXAMPLE
a(10) counts these 6 partitions: {10}, {9,1}, {7,3}, {7,2,1}, {6,4}, {5,4,1}.
MAPLE
g:= proc(n) option remember; `if`(n=0, 1, add(g(n-j)*add(
`if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
b:= proc(n, i, p) option remember; `if`(i*(i+1)/2<n, 0,
`if`(n=0, [x^p, 0], (f-> [add(coeff(f[1], x, j)*x^j
, j=i+1..degree(f[1])), f[2]+coeff(f[1], x, i)])(
b(n-i, min(n-i, i-1), p+1))+b(n, i-1, p)))
end:
a:= n-> g(n)-b(n$2, 0)[2]:
seq(a(n), n=0..55); # Alois P. Heinz, Mar 14 2024
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 14 2014
EXTENSIONS
a(0) changed to 1 by Alois P. Heinz, Mar 14 2024
STATUS
approved