The sequence S defined in A058540.

Terms

a(0) =0a(1) =0a(2) =1a(3) =3a(4) =12a(5) =48a(6) =217a(7) =1005a(8) =4878a(9) =24218a(10) =123021a(11) =634995a(12) =3323963a(13) =17596131a(14) =94053675a(15) =506865965a(16) =2751093957a(17) =15025119759a(18) =82511460766a(19) =455331632088