Convolution of partition numbers and Bell numbers.

Terms

a(0) =1a(1) =2a(2) =5a(3) =12a(4) =32a(5) =95a(6) =328a(7) =1294a(8) =5748a(9) =28152a(10) =149768a(11) =856130a(12) =5218107a(13) =33712600a(14) =229800588a(15) =1646316230a(16) =12355374717a(17) =96861192976a(18) =791258805462