Ranks of certain relations among Euler sums of weight n.

Terms

a(0) =1a(1) =3a(2) =6a(3) =14a(4) =29a(5) =60a(6) =123a(7) =249a(8) =503a(9) =1012a(10) =2032a(11) =4075a(12) =8164a(13) =16347a(14) =32719a(15) =65471a(16) =130986a(17) =262030a(18) =524137a(19) =1048376a(20) =2096887a(21) =4193953a(22) =8388143a(23) =16776600a(24) =33553616a(25) =67107783a(26) =134216296a(27) =268433559a(28) =536868399a(29) =1073738495