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a(0) = a(1) = 1; a(n) = [x^n] Product_{k=1..n-1} (1 + x^a(k))/(1 - x^a(k)).
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%I #4 Dec 11 2017 14:28:52

%S 1,1,2,6,8,10,14,18,26,34,46,58,74,90,114,138,174,210,260,310,378,446,

%T 536,626,748,870,1034,1198,1410,1622,1892,2162,2510,2858,3306,3754,

%U 4316,4878,5576,6274,7144,8014,9096,10178,11508,12838,14458,16078,18048,20018,22410,24802,27690,30578,34040

%N a(0) = a(1) = 1; a(n) = [x^n] Product_{k=1..n-1} (1 + x^a(k))/(1 - x^a(k)).

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F G.f. A(x) = Sum_{n>=0} a(n)*x^n satisfies A(x) = -x - 2*x^2 + Product_{n>=1} (1 + x^a(n))/(1 - x^a(n)).

%t a[n_] := a[n] = SeriesCoefficient[Product[(1 + x^a[k])/(1 - x^a[k]), {k, 1, n - 1}], {x, 0, n}]; a[0] = a[1] = 1; Table[a[n], {n, 0, 54}]

%Y Cf. A015128, A151945, A229362, A293806.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Dec 11 2017