Here a(n) is the number of binary strings having the maximum possible (fractional) weight -- that weight is given by A309093(n).
Table of n, a(n) for n=1..18.
Cf. A309093, A309078.
Sequence in context: A117855 A086442 A071407 * A109859 A128057 A128014
Adjacent sequences: A309091 A309092 A309093 * A309095 A309096 A309097
Jeffrey Shallit, Jul 12 2019