Number of increasing columns in all 2-compositions of n.

Terms

a(0) =0a(1) =1a(2) =5a(3) =24a(4) =104a(5) =432a(6) =1736a(7) =6820a(8) =26332a(9) =100308a(10) =377996a(11) =1411844a(12) =5234428a(13) =19285252a(14) =70670972a(15) =257766212a(16) =936336572a(17) =3388962884a(18) =12226547132a(19) =43983439684a(20) =157814634684a(21) =564917186372