The binomial transform of the swinging factorial (A056040).

Terms

a(0) =1a(1) =2a(2) =5a(3) =16a(4) =47a(5) =146a(6) =447a(7) =1380a(8) =4251a(9) =13102a(10) =40343a(11) =124136a(12) =381625a(13) =1172198a(14) =3597401a(15) =11031012a(16) =33798339a(17) =103477590a(18) =316581567a(19) =967900224a(20) =2957316429a(21) =9030317478a(22) =27558851565a(23) =84059345244a(24) =256265811333a(25) =780885245826