Number of n-element subsets of [2n] whose sum is a triangular number.

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =11a(5) =35a(6) =106a(7) =337a(8) =1112a(9) =3741a(10) =12821a(11) =44576a(12) =156862a(13) =557580a(14) =1999117a(15) =7221134a(16) =26253632a(17) =95996850a(18) =352798772a(19) =1302457652a(20) =4828002125a(21) =17962539164a(22) =67052864821a(23) =251066424023a(24) =942692613615