OFFSET
0,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..3000
FORMULA
a(n) ~ exp(Pi*(sqrt(2) + 1)*sqrt(n/6) + ((sqrt(2) - 1)*Pi)^2/48) * 2^(n - 9/4) / (3^(3/4) * n^(7/4)). - Vaclav Kotesovec, May 07 2019
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(binomial(n, j)*b(j)*combinat[numbpart](n-j), j=0..n):
seq(a(n), n=0..30); # Alois P. Heinz, Apr 26 2019
MATHEMATICA
nmax = 30; CoefficientList[Series[Sum[PartitionsP[i] x^i/i!, {i, 0, nmax}] Sum[PartitionsQ[j] x^j/j!, {j, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Binomial[n, k] PartitionsP[k] PartitionsQ[n - k], {k, 0, n}], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 26 2019
STATUS
approved