A328424 a(1) = 1; a(n) = Sum_{d|n, d < n} p(n/d) * a(d), where p = A000041 (partition numbers).

1, 2, 3, 9, 7, 23, 15, 50, 39, 70, 56, 187, 101, 195, 218, 420, 297, 625, 490, 949, 882, 1226, 1255, 2533, 2007, 2840, 3217, 4588, 4565, 6966, 6842, 10099, 10479, 13498, 15093, 21507, 21637, 27975, 31791, 41722, 44583, 58022, 63261, 80415, 90799, 110578, 124754

Offset: 1

Author

Ilya Gutkovskiy, Oct 15 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000041, A050354, A050369, A074206, A308076.

Programs

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

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