Terms at square positions in Pascal's triangle when in flattened form.

Terms

a(0) =1a(1) =1a(2) =2a(3) =1a(4) =5a(5) =15a(6) =1a(7) =126a(8) =10a(9) =220a(10) =715a(11) =15a(12) =12870a(13) =17a(14) =27132a(15) =15504a(16) =1540a(17) =1144066a(18) =1a(19) =5311735a(20) =80730a(21) =475020a(22) =54627300a(23) =32a(24) =1037158320a(25) =46376a(26) =254186856a(27) =854992152a(28) =82251a(29) =131282408400