Binomial convolution of the Floor-Sqrt transform of Catalan numbers.

Terms

a(0) =1a(1) =2a(2) =4a(3) =10a(4) =28a(5) =82a(6) =264a(7) =866a(8) =2984a(9) =10476a(10) =37500a(11) =135916a(12) =496242a(13) =1821384a(14) =6712394a(15) =24818020a(16) =92016874a(17) =342043052a(18) =1274461144a(19) =4759439600a(20) =17812520318a(21) =66803249358a(22) =251038475982a(23) =945202437760