OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
FORMULA
G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} p(k) * A(x^k).
a(n) ~ exp(Pi*sqrt(2*n/3)) / (4*sqrt(3)*n). - Vaclav Kotesovec, Oct 16 2019
MATHEMATICA
a[n_] := If[n == 1, n, Sum[If[d < n, PartitionsP[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 47}]
terms = 47; A[_] = 0; Do[A[x_] = x + Sum[PartitionsP[k] A[x^k], {k, 2, terms}] + O[x]^(terms + 1) // Normal, terms + 1]; CoefficientList[A[x], x] // Rest
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 15 2019
STATUS
approved