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 A118971 #43 Feb 15 2024 13:53:51
%S A118971 1,4,26,204,1771,16380,158224,1577532,16112057,167710664,1772645420,
%T A118971 18974357220,205263418941,2240623268512,24648785802336,
%U A118971 272994644359580,3041495503591365,34064252968167180,383302465665133014
%N A118971 a(n) = binomial(5*n+3,n)/(n+1).
%C A118971 A quadrisection of A118968.
%C A118971 For n >= 1, a(n-1) is the number of lattice paths from (0,0) to (4n,n) using only the steps (1,0) and (0,1) and which stay strictly below the line y = x/4 except at the path's endpoints. - _Lucas A. Brown_, Aug 21 2020
%C A118971 This is instance k = 4 of the family {c(k, n+1)}_{n>=0} given in a comment in A130564. - _Wolfdieter Lang_, Feb 04 2024
%H A118971 Michael De Vlieger, <a href="/A118971/b118971.txt">Table of n, a(n) for n = 0..924</a>
%H A118971 Paul Barry, <a href="https://arxiv.org/abs/2001.08799">Characterizations of the Borel triangle and Borel polynomials</a>, arXiv:2001.08799 [math.CO], 2020.
%H A118971 Elżbieta Liszewska and Wojciech Młotkowski, <a href="https://arxiv.org/abs/1907.10725">Some relatives of the Catalan sequence</a>, arXiv:1907.10725 [math.CO], 2019.
%H A118971 J. Sawada, J. Sears, A. Trautrim, and A. Williams, <a href="https://arxiv.org/abs/2308.12405">Demystifying our Grandparent's De Bruijn Sequences with Concatenation Trees</a>, arXiv:2308.12405 [math.CO], 2023.
%F A118971 G.f.: If the inverse series of y*(1-y)^4 is G(x) then A(x)=G(x)/x.
%F A118971 D-finite with recurrence 8*(4*n+1)*(2*n+1)*(4*n+3)*(n+1)*a(n) -5*(5*n+1)*(5*n+2)*(5*n+3)*(5*n-1)*a(n-1)=0. - _R. J. Mathar_, Nov 26 2012
%F A118971 a(n) = (4/5)*binomial(5*(n+1),n+1)/(5*(n+1)-1). - _Bruno Berselli_, Jan 17 2014
%F A118971 E.g.f.: 4F4(4/5,6/5,7/5,8/5; 5/4,3/2,7/4,2; 3125*x/256). - _Ilya Gutkovskiy_, Jan 23 2018
%F A118971 G.f.: 5F4([4,5,6,7,8]/5, [5,6,7,8]/4; (5^5/4^4)*x) = (4/(5*x))*(1 - 4F3([-1,1,2,3]/5, [1,2,3]/4; (5^5/4^4)*x)). - _Wolfdieter Lang_, Feb 15 2024
%t A118971 Table[4*Binomial[5n+3,n]/(4n+4),{n,0,30}] (* _Harvey P. Dale_, Apr 09 2012 *)
%Y A118971 Cf. A000108, A006013, A006632, A130564, A130565, A234466, A234513, A234573, A235340 (members of the same family).
%K A118971 easy,nonn
%O A118971 0,2
%A A118971 _Paul Barry_, May 07 2006