OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..n} A000009(k) * (n-k)^2.
G.f.: x*(1+x)/(1-x)^3 * Product_{k>=1} (1 + x^k).
a(n) ~ 4 * 3^(5/4) * n^(3/4) * exp(sqrt(n/3)*Pi) / Pi^3.
MAPLE
b:= proc(n) option remember; `if`(n=0, 1, add(b(n-j)*add(
`if`(d::odd, d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
a:= n-> add(b(n-j)*j^2, j=0..n):
seq(a(n), n=0..42); # Alois P. Heinz, Feb 09 2023
MATHEMATICA
Table[Sum[PartitionsQ[k]*(n-k)^2, {k, 0, n}], {n, 0, 60}]
CoefficientList[Series[x*(1+x)*QPochhammer[-1, x] / (2*(1-x)^3), {x, 0, 60}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Feb 09 2023
STATUS
approved