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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.

%I A259356 #16 Aug 16 2015 16:15:01
%S A259356 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,
%T A259356 210,6,0,132,5210,17816,15810,4596,406,7
%N 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.
%F A259356 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).
%F A259356 T(n+1,1) = A000108(n).
%e A259356 In table format, the first few rows:
%e A259356 {0},
%e A259356 {0,1},
%e A259356 {0,1,2},
%e A259356 {0,2,9,3},
%e A259356 {0,5,38,35,4},
%e A259356 ...
%e A259356 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:
%e A259356 \x.\y.x x
%e A259356 \x.\y.x y
%e A259356 \x.\y.y x
%e A259356 \x.\y.y y
%e A259356 (\x.x) (\y.y)
%e A259356 \x.(\y.y) x
%e A259356 \x.(\y.x) x
%e A259356 \x.x (\y.y)
%e A259356 \x.x (\y.x)
%Y A259356 Cf. A220894 (row sums), A000108.
%K A259356 nonn,tabl,more
%O A259356 0,6
%A A259356 _John Bodeen_, Jun 24 2015