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Number of closable Motzkin trees.
0

%I #18 Mar 29 2020 16:40:23

%S 0,1,1,2,5,11,26,65,163,417,1086,2858,7599,20391,55127,150028,410719,

%T 1130245,3124770,8675210,24175809,67603633,189633981,533463183,

%U 1504644945,4254179693,12055097308,34231674486,97392368007,277590288931,792528581088

%N Number of closable Motzkin trees.

%C From the Bodini-Tarau paper: a closable Motzkin tree is "the skeleton of at least one closed lambda term".

%H Olivier Bodini, Paul Tarau, <a href="https://arxiv.org/abs/1709.04302">On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms</a>, arXiv:1709.04302 [cs.PL], 2017.

%p f:= gfun:-rectoproc({

%p (384*n^2 +384*n) *a(n ) +

%p (-32*n^2-512*n-480) *a(n+1) +

%p (-368*n^2 -2192*n-2928) *a(n+2) +

%p (-56*n^2 -344*n-504) *a(n+3) +

%p (-4*n^2 +188*n+852) *a(n+4) +

%p (110*n^2 +1034*n+2328) *a(n+5) +

%p (-21*n^2 -201*n-390) *a(n+6) +

%p (-21*n^2 -327*n-1272) *a(n+7) +

%p (9*n^2 +153*n+648) *a(n+8) +

%p (-n^2 -19*n-90) *a(n+9) = 0,

%p a(0) = 0, a(1) = 0, a(2) = 1, a(3) = 1, a(4) = 2, a(5) = 5, a(6) = 11, a(7) = 26, a(8) = 65

%p }, a(n), remember): map(f, [$1..64]); # _Georg Fischer_, Mar 29 2020 (from the Bodini-Tarau paper)

%Y Cf. A000108, A001006, A135501.

%K nonn

%O 0,4

%A _Michael De Vlieger_, Feb 25 2018

%E More terms from _Georg Fischer_, Mar 29 2020