a(n) = (1/n!)*A001689(n).

Terms

a(0) =44a(1) =309a(2) =1214a(3) =3539a(4) =8544a(5) =18089a(6) =34754a(7) =61959a(8) =104084a(9) =166589a(10) =256134a(11) =380699a(12) =549704a(13) =774129a(14) =1066634a(15) =1441679a(16) =1915644a(17) =2506949a(18) =3236174a(19) =4126179a(20) =5202224a(21) =6492089a(22) =8026194a(23) =9837719a(24) =11962724a(25) =14440269a(26) =17312534a(27) =20624939a(28) =24426264