This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A281270 #52 Apr 11 2022 14:54:54
%S A281270 0,0,1,2,3,9,30,81,242,838,2799,9365,33616,122937,449698,1696724,
%T A281270 6558855,25559806,101294687,409363758,1673735259,6928460475,
%U A281270 29115833976,123835124242,532449210893,2317382872404,10199542298725,45345006540851,203704505953902,924427259637953,4234544300812834
%N A281270 a(n) is the number of closed BCK (a.k.a. affine) lambda terms of size n.
%C A281270 It appears that for n >= 1, a(n + 5) == a(n) (mod 5), a(n + 38*7) == a(n) (mod 7), a(n + 30*11) == a(n) (mod 11) and a(n + 288*17) == a(n) (mod 17). - _Peter Bala_, Apr 11 2022
%H A281270 Gheorghe Coserea, <a href="/A281270/b281270.txt">Table of n, a(n) for n = 0..201</a>
%H A281270 O. Bodini, D. Gardy, and A. Jacquot, <a href="https://doi.org/10.1016/j.tcs.2013.01.008">Asymptotics and random sampling for BCI and BCK lambda terms</a>, Theor. Comput. Sci. 502: 227-238 (2013).
%H A281270 Katarzyna Grygiel, Pawel M. Idziak and Marek Zaionc, <a href="http://arxiv.org/abs/1112.0643">How big is BCI fragment of BCK logic</a>, arXiv preprint arXiv:1112.0643 [cs.LO], 2011. (the authors of the paper incorrectly identified this sequence as A073950)
%H A281270 Pierre Lescanne, <a href="https://arxiv.org/abs/1702.03085">Quantitative aspects of linear and affine closed lambda term</a>, arXiv:1702.03085 [cs.DM], 2017.
%F A281270 a(n) = 1 + a(n-1) + 2*Sum_{k=2..n-3} k*a(k) + Sum_{k=2..n-3} a(k)*a(n-1-k) for n>=2.
%F A281270 0 = 2*x^4*y' + (x-x^2)*y^2 - (1-x)^2*y + x^2, where y(x) is the g.f.
%F A281270 a(3*n+1) = Sum_{k=0..n-1} binomial(3*n,3*k+1)*A062980(k).
%e A281270 A(x) = x^2 + 2*x^3 + 3*x^4 + 9*x^5 + 30*x^6 + 81*x^7 + 242*x^8 + ...
%t A281270 a[0] = a[1] = 0; a[n_] := a[n] = 1 + a[n - 1] + 2 Sum[ k a[k], {k, 2, n - 3}] + Sum[a[k] a[n - 1 - k], {k, 2, n - 3}]; Table[a@ n, {n, 0, 30}] (* _Michael De Vlieger_, Apr 02 2017 *)
%o A281270 (PARI)
%o A281270 seq(N) = {
%o A281270 my(a = vector(N));
%o A281270 for (n=2, N, my(s1 = sum(k=2, n-3, k*a[k]));
%o A281270 a[n] = 1 + a[n-1] + 2*s1 + sum(k=2, n-3, a[k]*a[n-1-k]));
%o A281270 concat(0,a);
%o A281270 };
%o A281270 seq(30)
%o A281270 \\ test: y = Ser(seq(201)); 0 == 2*x^4*y' + (x-x^2)*y^2 - (1-x)^2*y + x^2
%Y A281270 Cf. A062980, A262301, A267827.
%K A281270 nonn
%O A281270 0,4
%A A281270 _Gheorghe Coserea_, Apr 02 2017
%E A281270 Name clarified by _Pierre Lescanne_, May 19 2017