a(n) = Sum_{d|n} mu(n/d) * binomial(3*d,d) / (2*d+1).

Terms

a(0) =1a(1) =2a(2) =11a(3) =52a(4) =272a(5) =1414a(6) =7751a(7) =43208a(8) =246663a(9) =1430440a(10) =8414639a(11) =50065628a(12) =300830571a(13) =1822758766a(14) =11124755380a(15) =68328711696a(16) =422030545334