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A262301 Number of normal linear lambda terms of size n with no free variables.

%I A262301 #46 May 31 2025 18:37:41
%S A262301 1,3,26,367,7142,176766,5304356,186954535,7566084686,345664350778,
%T A262301 17592776858796,986961816330662,60502424162842876,4023421969420255644,
%U A262301 288464963899330354104,22180309834307193611287,1820641848410408158704734,158897008602951290424279330
%N A262301 Number of normal linear lambda terms of size n with no free variables.
%H A262301 Gheorghe Coserea, <a href="/A262301/b262301.txt">Table of n, a(n) for n = 1..100</a>
%H A262301 Paul Tarau, Valeria de Paiva, <a href="https://arxiv.org/abs/2009.10241">Deriving Theorems in Implicational Linear Logic, Declaratively</a>, arXiv:2009.10241 [cs.LO], 2020. See also <a href="https://vcvpaiva.github.io/includes/pubs/2020-tarau.pdf">Github</a>, (2020).
%H A262301 Noam Zeilberger, <a href="http://arxiv.org/abs/1509.07596">Counting isomorphism classes of beta-normal linear lambda terms</a>, arXiv:1509.07596 [cs.LO], 2015.
%H A262301 Wikipedia, <a href="https://en.wikipedia.org/wiki/Lambda_calculus">Lambda calculus</a>
%F A262301 A(x) = F(x,0), where A(x) = Sum_{n>=1} a(n)*x^n and F(x,t) satisfies F = x*t/(1-F) + deriv(F,t), with F(0,t)=0, deriv(F,x)(0,t)=1+t. - _Gheorghe Coserea_, Apr 01 2017
%e A262301 A(x) = x + 3*x^2 + 26*x^3 + 367*x^4 + 7142*x^5 + ...
%t A262301 terms = 18; F[_, _] = 0;
%t A262301 Do[F[x_, t_] = Series[x t/(1-F[x, t]) + D[F[x, t], t], {x, 0, terms}, {t, 0, terms}] // Normal, {2 terms}];
%t A262301 CoefficientList[F[x, 0], x][[2 ;; terms+1]] (* _Jean-François Alcover_, Sep 02 2018, after _Gheorghe Coserea_ *)
%o A262301 (PARI)
%o A262301 F(N) = {
%o A262301   my(x='x+O('x^N), t='t, F0=x, F1=0, n=1);
%o A262301   while(n++,
%o A262301     F1 = x*t/(1-F0) + deriv(F0,t);
%o A262301     if (F1 == F0, break()); F0 = F1;);
%o A262301   F0;
%o A262301 };
%o A262301 seq(N) = Vec(subst(F(N+1), 't, 0));
%o A262301 seq(18) \\ _Gheorghe Coserea_, Apr 01 2017
%Y A262301 Column 0 of A318110.
%Y A262301 Cf. A062980, A267827.
%K A262301 nonn
%O A262301 1,2
%A A262301 _N. J. A. Sloane_, Sep 30 2015
%E A262301 More terms from _Gheorghe Coserea_, Apr 01 2017