%I #4 Nov 21 2019 22:16:24

%S 1,1,2,3,3,8,5,11,12,16,12,37,18,32,39,55,38,90,54,105,96,113,104,236,

%T 151,201,232,301,256,450,340,517,496,588,615,988,760,972,1054,1395,

%U 1260,1766,1610,2078,2240,2512,2590,3653,3289,4029,4249,5038,5120,6526

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

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

%t 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}]

%t 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

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

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Nov 21 2019