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 A116093 #30 Sep 08 2022 08:45:24
%S A116093 1,-2,0,16,-56,48,384,-1920,3168,8512,-66560,161280,113920,-2224640,
%T A116093 7311360,-3354624,-69253632,306754560,-408059904,-1898029056,
%U A116093 12054196224,-25377005568,-38874316800,443400781824,-1289598418944,-52751204352,15086928789504,-58620595404800
%N A116093 Expansion of 1/sqrt(1+4*x+12*x^2).
%C A116093 Apart from signs identical this is to A098336. - _Joerg Arndt_, Jun 30 2013
%C A116093 Fourth binomial transform of the expansion of 1/sqrt(1-4*x+12*x^2), A098336.
%H A116093 Seiichi Manyama, <a href="/A116093/b116093.txt">Table of n, a(n) for n = 0..1000</a>
%H A116093 Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Szalay/szalay42.html">Diagonal Sums in the Pascal Pyramid, II: Applications</a>, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.
%F A116093 E.g.f.: exp(-2*x)*Bessel_I(0,2*sqrt(-2)*x).
%F A116093 a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)*binomial(n-k,k)(-2)^(n-k).
%F A116093 D-finite with recurrence: n*a(n) +2*(2*n-1)*a(n-1) +12*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 07 2012
%F A116093 G.f.: G(0), where G(k)= 1 - 2*x*(1+3*x)*(4*k+1)/( 2*k+1 - x*(1+3*x)*(2*k+1)*(4*k+3)/(x*(1+3*x)*(4*k+3) - (k+1)/G(k+1) )); (continued fraction). - _Sergei N. Gladkovskii_, Jun 30 2013
%t A116093 CoefficientList[Series[1/Sqrt[1+4x+12x^2],{x,0,30}],x] (* _Harvey P. Dale_, Oct 15 2014 *)
%o A116093 (PARI) my(x='x+O('x^30)); Vec(1/sqrt(1+4*x+12*x^2)) \\ _G. C. Greubel_, May 10 2019
%o A116093 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(1+4*x+12*x^2) )); // _G. C. Greubel_, May 10 2019
%o A116093 (Sage) (1/sqrt(1+4*x+12*x^2)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 10 2019
%Y A116093 Column 2 of A307819.
%Y A116093 Cf. A098336.
%K A116093 easy,sign
%O A116093 0,2
%A A116093 _Paul Barry_, Feb 04 2006