Triangular numbers (A000217) with arithmetic derivative (A003415) a palindrome (A002113).

Terms

a(0) =0a(1) =1a(2) =3a(3) =6a(4) =10a(5) =15a(6) =136a(7) =153a(8) =231a(9) =741a(10) =1711a(11) =11026a(12) =22366a(13) =99681a(14) =104653a(15) =593505a(16) =1348903a(17) =1378630a(18) =1886653a(19) =3098805a(20) =4388203a(21) =4474536a(22) =24587578a(23) =26626753a(24) =32092066a(25) =45825951a(26) =132804253a(27) =165283471a(28) =197239591a(29) =355657785