T(n,k) is the number of order-decreasing and order-preserving partial transformations (of an n-chain) of width (width(alpha) = |Dom(alpha)|) and waist (waist(alpha) = max(Im(alpha))) both equal to k.

A145034

T(n,k) is the number of order-decreasing and order-preserving partial transformations (of an n-chain) of width (width(alpha) = |Dom(alpha)|) and waist (waist(alpha) = max(Im(alpha))) both equal to k.

Terms

    a(0) =1a(1) =1a(2) =1a(3) =1a(4) =2a(5) =1a(6) =1a(7) =3a(8) =4a(9) =2a(10) =1a(11) =4a(12) =9a(13) =12a(14) =5a(15) =1a(16) =5a(17) =16a(18) =36a(19) =40a(20) =14a(21) =1a(22) =6a(23) =25a(24) =80a(25) =150a(26) =140a(27) =42a(28) =1a(29) =7

External references