Diagonal sums of correlation triangle of central binomial coefficients.

Terms

a(0) =1a(1) =2a(2) =8a(3) =25a(4) =90a(5) =312a(6) =1145a(7) =4186a(8) =15640a(9) =58681a(10) =222298a(11) =845848a(12) =3235385a(13) =12418650a(14) =47827992a(15) =184688185a(16) =714884186a(17) =2772776984a(18) =10774163001a(19) =41932100698a(20) =163430680600a(21) =637793652281