a(n) = Sum_{k=0..n} binomial(n+1,k+1)*A001003(k).

Terms

a(0) =1a(1) =3a(2) =9a(3) =33a(4) =145a(5) =713a(6) =3745a(7) =20513a(8) =115713a(9) =667329a(10) =3916033a(11) =23305857a(12) =140327681a(13) =853262465a(14) =5231925761a(15) =32313686529a(16) =200843829249