Decomposition of Stirling's S(n,2) based on associated numeric partitions.

Terms

a(0) =0a(1) =1a(2) =3a(3) =8a(4) =3a(5) =30a(6) =20a(7) =144a(8) =90a(9) =40a(10) =840a(11) =504a(12) =420a(13) =5760a(14) =3360a(15) =2688a(16) =1260a(17) =45360a(18) =25920a(19) =20160a(20) =18144a(21) =403200a(22) =226800a(23) =172800a(24) =151200a(25) =72576a(26) =3991680a(27) =2217600a(28) =1663200a(29) =1425600