a(n) = binomial(F(n), 2) where F(n) = A000045(n).

Terms

a(0) =0a(1) =0a(2) =0a(3) =1a(4) =3a(5) =10a(6) =28a(7) =78a(8) =210a(9) =561a(10) =1485a(11) =3916a(12) =10296a(13) =27028a(14) =70876a(15) =185745a(16) =486591a(17) =1274406a(18) =3337236a(19) =8738290a(20) =22879230a(21) =59901985a(22) =156830905a(23) =410597496a(24) =1074972528a(25) =2814337800a(26) =7368069528a(27) =19289917153a(28) =50501756955a(29) =132215475106