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 A098411 #32 Aug 06 2024 04:43:36
%S A098411 1,8,72,704,7264,77568,847104,9394176,105334272,1190899712,
%T A098411 13551235072,154997784576,1780378353664,20522842062848,
%U A098411 237284128063488,2750571189633024,31956067676454912,371997834879172608,4337957919010062336,50664706036388069376,592558533060795039744
%N A098411 Expansion of 1/(sqrt(1-4x)sqrt(1-12x)).
%C A098411 Nguyen and Taggart (see link) conjecture: det[a(i+j) for i,j=0..n] = b(n)*b(n+1)/2 with b(n) = A139685(n). - _Peter Luschny_, May 19 2015
%H A098411 Vincenzo Librandi, <a href="/A098411/b098411.txt">Table of n, a(n) for n = 0..200</a>
%H A098411 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.
%H A098411 H. D. Nguyen, D. Taggart, <a href="https://citeseerx.ist.psu.edu/pdf/8f2f36f22878c984775ed04368b8893879b99458">Mining the OEIS: Ten Experimental Conjectures</a>, 2013; Mentions this sequence. - From _N. J. A. Sloane_, Mar 16 2014
%F A098411 G.f.: 1/sqrt(1-16x+48x^2).
%F A098411 E.g.f.: exp(8x)*BesselI(0, 4x).
%F A098411 a(n) = Sum_{k=0..n} 3^k*binomial(2k, k)*binomial(2(n-k), n-k).
%F A098411 D-finite with recurrence: n*a(n) +8*(1-2*n)*a(n-1) +48*(n-1)*a(n-2)=0. - _R. J. Mathar_, Sep 26 2012
%F A098411 a(n) ~ sqrt(3)*12^n/sqrt(2*Pi*n). - _Vaclav Kotesovec_, Oct 15 2012
%F A098411 a(n) = 4^n*hypergeometric([-n, 1/2], [1], -2). - _Peter Luschny_, May 19 2015
%t A098411 Table[SeriesCoefficient[1/(Sqrt[1-4*x]*Sqrt[1-12*x]),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 15 2012 *)
%o A098411 (PARI) x='x+O('x^66); Vec(1/sqrt(1-16*x+48*x^2)) \\ _Joerg Arndt_, May 11 2013
%o A098411 (Sage)
%o A098411 a = lambda n: 4^n*hypergeometric([-n, 1/2], [1], -2)
%o A098411 [simplify(a(n)) for n in range(23)] # _Peter Luschny_, May 19 2015
%Y A098411 Cf. A098410, A139685.
%K A098411 easy,nonn
%O A098411 0,2
%A A098411 _Paul Barry_, Sep 07 2004