

A259356


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


0



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
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OFFSET

0,6


LINKS

Table of n, a(n) for n=0..35.


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(n1,k1,b+1) + Sum_{i=0..n1} Sum_{j=0..k} T(i,j,b) * T(n1i,kj,b).
T(n+1,1) = A000108(n).


EXAMPLE

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.
Sequence in context: A212026 A246003 A242052 * A137302 A265607 A091518
Adjacent sequences: A259353 A259354 A259355 * A259357 A259358 A259359


KEYWORD

nonn,tabl,more


AUTHOR

John Bodeen, Jun 24 2015


STATUS

approved



