Total number of partitions of [n-s] whose block maxima sum to s, summed over all s.

Terms

a(0) =1a(1) =0a(2) =1a(3) =0a(4) =1a(5) =1a(6) =1a(7) =1a(8) =3a(9) =2a(10) =3a(11) =6a(12) =5a(13) =9a(14) =14a(15) =13a(16) =20a(17) =40a(18) =31a(19) =56a(20) =86a(21) =105a(22) =127a(23) =227a(24) =244a(25) =394a(26) =520a(27) =665a(28) =911a(29) =1536