A304991 a(n) = A000041(n) * A000009(n).

1, 1, 2, 6, 10, 21, 44, 75, 132, 240, 420, 672, 1155, 1818, 2970, 4752, 7392, 11286, 17710, 26460, 40128, 60192, 89178, 130520, 192150, 278036, 401940, 577920, 825396, 1168640, 1658784, 2326280, 3256110, 4544064, 6302720, 8706555, 12008636, 16444120, 22476960

Offset: 0

Author

Vaclav Kotesovec, May 23 2018

Keywords

• nonn

Crossrefs

Cf. A000009, A000041, A015128.

Programs

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-> b(n)*combinat[numbpart](n):
seq(a(n), n=0..40);  # Alois P. Heinz, May 23 2023

Mathematica

Table[PartitionsP[n]*PartitionsQ[n], {n, 0, 50}]

Formula

a(n) ~ exp(Pi*(1+sqrt(2))*sqrt(n/3)) / (16*3^(3/4)*n^(7/4)).