Number of partitions of floor(n^2/2) with at most n parts and maximal height n.

Terms

a(0) =1a(1) =1a(2) =2a(3) =3a(4) =8a(5) =20a(6) =58a(7) =169a(8) =526a(9) =1667a(10) =5448a(11) =18084a(12) =61108a(13) =208960a(14) =723354a(15) =2527074a(16) =8908546a(17) =31630390a(18) =113093022a(19) =406680465a(20) =1470597342a(21) =5342750699a(22) =19499227828a(23) =71442850111a(24) =262754984020a(25) =969548468960