The main diagonal of the array of A141425 and its higher order differences.

Terms

a(0) =1a(1) =2a(2) =1a(3) =-7a(4) =-23a(5) =-1a(6) =7a(7) =-103a(8) =-251a(9) =-133a(10) =-149a(11) =-1387a(12) =-3143a(13) =-3001a(14) =-4913a(15) =-19663a(16) =-42611a(17) =-55693a(18) =-101549a(19) =-291667a(20) =-612863a(21) =-960001a(22) =-1831433a(23) =-4460023a(24) =-9185771a(25) =-15980053a(26) =-31162949a(27) =-69500347a(28) =-141392183a(29) =-261261001