a(n) is the largest path count within the (right-aligned Ferrers plots of the) partitions of n.

Terms

a(0) =1a(1) =1a(2) =1a(3) =2a(4) =2a(5) =3a(6) =3a(7) =5a(8) =6a(9) =7a(10) =9a(11) =10a(12) =14a(13) =16a(14) =19a(15) =23a(16) =28a(17) =32a(18) =42a(19) =47a(20) =56a(21) =66a(22) =76a(23) =90a(24) =107a(25) =132a(26) =146a(27) =174a(28) =202a(29) =230