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%I #10 Jul 28 2021 14:19:03
%S 0,0,1,0,3,3,18,39,157,459,1668,5503,19638,68325,245144,876438,
%T 3177651,11549939,42307920,155555733,574881920,2132231076,7938771624,
%U 29651189637,111086480106,417305224917,1571633677078,5932720163529,22443721850064,85075094996719,323086777251300
%N Complement of A187430 in A000108.
%C Related to the decomposition of A000108 as the sum of A055113 and A111160.
%F G.f. y(x) satisfies x y^4 + 2 x^2 y^2 + x^3 + 3 x y^2 + y^3 - x y = 0.
%o (Sage)
%o N = 30
%o x = (PowerSeriesRing(QQ, 'x').0).O(N + 1)
%o f = (x*(1-x^2)^2/(1+x^3)^2).reverse()
%o g = sum(catalan_number(n)*x**n for n in range(N + 1)).O(N + 1)
%o list(x*g-f)
%Y Cf. A000108, A055113, A111160, A187430.
%K nonn
%O 0,5
%A _F. Chapoton_, Jul 14 2021
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