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 A228338 #15 May 25 2021 12:28:51
%S A228338 5,9,19,43,102,250,628,1608,4181,11009,29295,78655,212815,579675,
%T A228338 1588245,4374285,12103407,33628827,93786969,262450881,736710360,
%U A228338 2073834420,5853011850,16558618510,46949351275,133390812255,379708642289,1082797114049,3092894319078,8848275403642
%N A228338 Third diagonal of Catalan difference table (A059346).
%H A228338 G. C. Greubel, <a href="/A228338/b228338.txt">Table of n, a(n) for n = 0..1000</a>
%H A228338 Jocelyn Quaintance and Harris Kwong, <a href="http://www.emis.de/journals/INTEGERS/papers/n29/n29.Abstract.html">A combinatorial interpretation of the Catalan and Bell number difference tables</a>, Integers, 13 (2013), #A29.
%F A228338 From _Vaclav Kotesovec_, Feb 14 2014: (Start)
%F A228338 Recurrence: (n+4)*a(n) = (2*n+7)*a(n-1) + 3*(n-1)*a(n-2).
%F A228338 G.f.: -(x+1)^(5/2)*sqrt(1-3*x)/(2*x^4)-1/2*(-1-x+3*x^2+7*x^3)/x^4.
%F A228338 a(n) ~ 8 * 3^(n+3/2) / (sqrt(Pi) * n^(3/2)). (End)
%F A228338 a(n) = 5*(-1)^n*hypergeom([7/2, -n], [5], 4). - _Peter Luschny_, May 25 2021
%p A228338 a := n -> 5*(-1)^n*hypergeom([7/2, -n], [5], 4):
%p A228338 seq(simplify(a(n)), n=0..29); # _Peter Luschny_, May 25 2021
%t A228338 CoefficientList[Series[-(x+1)^(5/2)*Sqrt[1-3*x]/(2*x^4)-1/2*(- 1 - x + 3*x^2 + 7*x^3)/x^4, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 14 2014 *)
%o A228338 (PARI) x='x+O('x^50); Vec(-(x+1)^(5/2)*sqrt(1-3*x)/(2*x^4)-1/2*(-1-x+3*x^2+7*x^3)/x^4) \\ _G. C. Greubel_, May 31 2017
%Y A228338 Cf. A059346, A001006, A005043, A005554.
%K A228338 nonn
%O A228338 0,1
%A A228338 _N. J. A. Sloane_, Aug 29 2013
%E A228338 Terms a(21) onward added by _G. C. Greubel_, May 31 2017