a(n) = floor(sum_{k>=0} k^n /(k!)^3); related to generalized Bell numbers.

Terms

a(0) =2a(1) =1a(2) =1a(3) =2a(4) =3a(5) =6a(6) =12a(7) =28a(8) =68a(9) =176a(10) =484a(11) =1409a(12) =4334a(13) =14002a(14) =47357a(15) =167157a(16) =614297a(17) =2345730a(18) =9290084a(19) =38092233a(20) =161436136a(21) =706061825a(22) =3182452003a(23) =14764717643a(24) =70429572474a(25) =345075959701