A259356 Triangle T(n,k) read by rows: T(n,k) is the number of closed lambda-terms of size n with size 0 for the variables and k abstractions.

0, 0, 1, 0, 1, 2, 0, 2, 9, 3, 0, 5, 38, 35, 4, 0, 14, 181, 284, 95, 5, 0, 42, 938, 2225, 1320, 210, 6, 0, 132, 5210, 17816, 15810, 4596, 406, 7

Offset: 0

Author

John Bodeen, Jun 24 2015

Keywords

• nonn
• tabl
• more

Examples

			In table format, the first few rows:
{0},
{0,1},
{0,1,2},
{0,2,9,3},
{0,5,38,35,4},
...
For n=3,k=2 we have the number of closed lambda terms of size three with exactly two abstractions, T(3,2,0) = 9:
\x.\y.x x
\x.\y.x y
\x.\y.y x
\x.\y.y y
(\x.x) (\y.y)
\x.(\y.y) x
\x.(\y.x) x
\x.x (\y.y)
\x.x (\y.x)
		

Crossrefs

Cf. A220894 (row sums), A000108.

Formula

T(n,k) = T(n,k,0) where T(n,k,b) where n is size, k is number of abstractions, and b is number of free variables, T(0,0,b) = b, and T(n,k,b) = T(n-1,k-1,b+1) + Sum_{i=0..n-1} Sum_{j=0..k} T(i,j,b) * T(n-1-i,k-j,b).

T(n+1,1) = A000108(n).