a(n) = A000166(floor(n/2)) if n is even otherwise A000240(floor((n + 1)/2)).

Terms

a(0) =1a(1) =1a(2) =0a(3) =0a(4) =1a(5) =3a(6) =2a(7) =8a(8) =9a(9) =45a(10) =44a(11) =264a(12) =265a(13) =1855a(14) =1854a(15) =14832a(16) =14833a(17) =133497a(18) =133496a(19) =1334960a(20) =1334961a(21) =14684571a(22) =14684570a(23) =176214840a(24) =176214841a(25) =2290792933a(26) =2290792932a(27) =32071101048a(28) =32071101049a(29) =481066515735