A329803 - OEIS

A329803

a(1) = 1; a(n) = Sum_{d|n, d < n} q(n/d) * a(d), where q() = A000009.

1, 1, 2, 3, 3, 8, 5, 11, 12, 16, 12, 37, 18, 32, 39, 55, 38, 90, 54, 105, 96, 113, 104, 236, 151, 201, 232, 301, 256, 450, 340, 517, 496, 588, 615, 988, 760, 972, 1054, 1395, 1260, 1766, 1610, 2078, 2240, 2512, 2590, 3653, 3289, 4029, 4249, 5038, 5120, 6526

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..54.

FORMULA

G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} q(k) * A(x^k).

MATHEMATICA

a[n_] := If[n == 1, n, Sum[If[d < n, PartitionsQ[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 1, 54}]

nmax = 54; A[_] = 0; Do[A[x_] = x + Sum[PartitionsQ[k] A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

CROSSREFS

Cf. A000009, A050354, A050369, A074206, A308076, A328424.