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a(1) = 1; a(n > 1) = Sum_{0 < k < n} (-1)^(n - k - 1) a(n - k) Sum_{d|k} a(d).
5

%I #7 Aug 12 2018 16:10:30

%S 1,1,1,1,2,2,5,6,11,14,23,26,51,70,114,147,237,314,516,715,1118,1549,

%T 2353,3252,5011,7235,10724,15142,22504,32506,47770,69173,100980,

%U 146657,212504,308563,448256,658037,946166,1373739,1988283,2919185,4197886,6118850

%N a(1) = 1; a(n > 1) = Sum_{0 < k < n} (-1)^(n - k - 1) a(n - k) Sum_{d|k} a(d).

%t a[n_]:=a[n]=If[n==1,1,Sum[(-1)^(n-k-1)*a[n-k]*Sum[a[d],{d,Divisors[k]}],{k,n-1}]];

%t Array[a,50]

%Y Cf. A001003, A001678, A002033, A003238, A052893, A053492, A067824, A167865, A214577, A277996, A280000, A317875.

%Y Cf. A317876, A317877, A317878, A317879, A317880, A317881.

%Y Cf. A317882, A317883, A317884, A317885.

%K nonn

%O 1,5

%A _Gus Wiseman_, Aug 09 2018