Number of multiset partitions of integer partitions of n such that all blocks are gapless.

Terms

a(0) =1a(1) =1a(2) =3a(3) =6a(4) =13a(5) =24a(6) =49a(7) =88a(8) =166a(9) =297a(10) =534a(11) =932a(12) =1635a(13) =2796a(14) =4782a(15) =8060a(16) =13521a(17) =22438a(18) =37080a(19) =60717a(20) =98979a(21) =160216a(22) =258115a(23) =413382a(24) =659177a(25) =1045636a(26) =1651891a(27) =2597849a(28) =4069708a(29) =6349677