a(n) = Sum_{k = 1..n} T(k,k-1), where T is the array defined in A024996.

Terms

a(0) =1a(1) =3a(2) =6a(3) =12a(4) =31a(5) =83a(6) =233a(7) =661a(8) =1893a(9) =5445a(10) =15720a(11) =45510a(12) =132069a(13) =384049a(14) =1118822a(15) =3264644a(16) =9539789a(17) =27913085a(18) =81769238a(19) =239794424a(20) =703906721a(21) =2068153901a(22) =6081507833a(23) =17896695833a(24) =52703944967a(25) =155310270103a(26) =457956633828