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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, 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 (list; table; graph; refs; listen; history; text; internal format)
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(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).

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

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Last modified October 19 20:05 EDT 2018. Contains 316378 sequences. (Running on oeis4.)