a(n) is the sum of the squares of diameters of all nonempty subsets of {1,2,...,n}.

Terms

a(0) =0a(1) =1a(2) =10a(3) =55a(4) =228a(5) =801a(6) =2526a(7) =7387a(8) =20440a(9) =54229a(10) =139218a(11) =348111a(12) =851916a(13) =2047945a(14) =4849606a(15) =11337667a(16) =26214336a(17) =60030909a(18) =136314810a(19) =307232695a(20) =687865780a(21) =1530920881a(22) =3388997550a(23) =7465861035a(24) =16374562728a(25) =35769024421a(26) =77846282146a(27) =168845901727