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 A059348 #18 Aug 31 2025 06:17:47
%S A059348 2,2,3,4,7,10,19,28,56,84,174,264,561,858,1859,2860,6292,9724,21658,
%T A059348 33592,75582,117572,266798,416024,950912,1485800,3417340,5348880,
%U A059348 12369285,19389690,45052515,70715340,165002460,259289580,607283490
%N A059348 Third diagonal of array in A059347.
%C A059348 Same as A104722 except for leading term (both have rational g.f.s). - _R. J. Mathar_ and _Franklin T. Adams-Watters_, May 19 2008
%H A059348 G. C. Greubel, <a href="/A059348/b059348.txt">Table of n, a(n) for n = 2..1000</a>
%H A059348 F. R. Bernhart, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00054-0">Catalan, Motzkin and Riordan numbers</a>, Discr. Math., 204 (1999), 73-112.
%F A059348 G.f.: 1 + ( (1 + x)*(1 - sqrt(1 - 4*x^2))/(2*x^2))^2. - _G. C. Greubel_, Jan 08 2017
%F A059348 a(n) ~ (9 + (-1)^n) * 2^(n - 3/2) / (sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Aug 31 2025
%t A059348 CoefficientList[Series[1 + ( (1 + x)*(1 - Sqrt[1 - 4*x^2])/(2*x^2))^2, {x, 0, 50}], x] (* _G. C. Greubel_, Jan 08 2017 *)
%o A059348 (PARI) Vec( 1 + ( (1 + x)*(1 - sqrt(1 - 4*x^2))/(2*x^2))^2 + O(x^25)) \\ _G. C. Greubel_, Jan 08 2017
%Y A059348 Cf. A059347, A104722.
%K A059348 nonn,changed
%O A059348 2,1
%A A059348 _N. J. A. Sloane_, Jan 27 2001