Convergent of an infinite product of Pascal's triangles aerated by rows.

Terms

a(0) =1a(1) =1a(2) =2a(3) =4a(4) =8a(5) =16a(6) =33a(7) =71a(8) =160a(9) =376a(10) =912a(11) =2256a(12) =5633a(13) =14093a(14) =35170a(15) =87344a(16) =215680a(17) =529568a(18) =1293633a(19) =3146515a(20) =7627208a(21) =18441476a(22) =44510160a(23) =107310480a(24) =258566402a(25) =622900466a(26) =1500717220a(27) =3616471960a(28) =8717948688a(29) =21023129472