a(n) = (A388291(n)^2 - 1)/24.

Terms

a(0) =0a(1) =1a(2) =7a(3) =35a(4) =330a(5) =1190a(6) =2262a(7) =7812a(8) =40426a(9) =73151a(10) =106267a(11) =349692a(12) =728365a(13) =1373295a(14) =2382030a(15) =3432997a(16) =9004975a(17) =34217652a(18) =46651605a(19) =77979755a(20) =111116370a(21) =234531276a(22) =388468927a(23) =760917032a(24) =1584781276a(25) =3618302051a(26) =7575315805a(27) =10391390352a(28) =11017977685a(29) =35710034801