cp's OEIS Frontend

A300125 Number of closable Motzkin trees.

%I A300125 #18 Mar 29 2020 16:40:23
%S A300125 0,1,1,2,5,11,26,65,163,417,1086,2858,7599,20391,55127,150028,410719,
%T A300125 1130245,3124770,8675210,24175809,67603633,189633981,533463183,
%U A300125 1504644945,4254179693,12055097308,34231674486,97392368007,277590288931,792528581088
%N A300125 Number of closable Motzkin trees.
%C A300125 From the Bodini-Tarau paper: a closable Motzkin tree is "the skeleton of at least one closed lambda term".
%H A300125 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 A300125 f:= gfun:-rectoproc({
%p A300125   (384*n^2 +384*n)        *a(n  ) +
%p A300125   (-32*n^2-512*n-480)     *a(n+1) +
%p A300125   (-368*n^2 -2192*n-2928) *a(n+2) +
%p A300125   (-56*n^2 -344*n-504)    *a(n+3) +
%p A300125   (-4*n^2 +188*n+852)     *a(n+4) +
%p A300125   (110*n^2 +1034*n+2328)  *a(n+5) +
%p A300125   (-21*n^2 -201*n-390)    *a(n+6) +
%p A300125   (-21*n^2 -327*n-1272)   *a(n+7) +
%p A300125   (9*n^2 +153*n+648)      *a(n+8) +
%p A300125   (-n^2 -19*n-90)         *a(n+9) = 0,
%p A300125   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 A300125 }, a(n), remember): map(f, [$1..64]); # _Georg Fischer_, Mar 29 2020 (from the Bodini-Tarau paper)
%Y A300125 Cf. A000108, A001006, A135501.
%K A300125 nonn
%O A300125 0,4
%A A300125 _Michael De Vlieger_, Feb 25 2018
%E A300125 More terms from _Georg Fischer_, Mar 29 2020