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 A098455 #30 Aug 30 2025 10:13:00
%S A098455 1,2,24,128,1096,7632,60864,461568,3648096,28551872,226695424,
%T A098455 1799989248,14380907776,115126211072,924791445504,7444100947968,
%U A098455 60057602459136,485388465196032,3929580292706304,31858982479331328,258641677679947776,2102242140708298752
%N A098455 Expansion of 1/sqrt(1-4*x-36*x^2).
%C A098455 Define Q(n,x) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(2(n-k),n) * x^(n-2k). Then a(n) = 3^n*Q(n,1/3). A084770(n) is 2^n*Q(n,1/2). Central coefficient of (1+2*x+10*x^2)^n.
%H A098455 Vincenzo Librandi, <a href="/A098455/b098455.txt">Table of n, a(n) for n = 0..200</a>
%H A098455 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 A098455 E.g.f.: exp(2*x) * BesselI(0, 2*sqrt(10)*x).
%F A098455 a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)*binomial(2(n-k), n)*9^k.
%F A098455 D-finite with recurrence: n*a(n) = 2*(2*n-1)*a(n-1) + 36*(n-1)*a(n-2). - _Vaclav Kotesovec_, Oct 15 2012
%F A098455 a(n) ~ sqrt(50+5*sqrt(10))*(2+2*sqrt(10))^n/(10*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 15 2012
%F A098455 From _Seiichi Manyama_, Aug 30 2025: (Start)
%F A098455 a(n) = Sum_{k=0..n} (1-3*i)^k * (1+3*i)^(n-k) * binomial(n,k)^2, where i is the imaginary unit.
%F A098455 a(n) = Sum_{k=0..floor(n/2)} 10^k * 2^(n-2*k) * binomial(n,2*k) * binomial(2*k,k). (End)
%t A098455 Table[SeriesCoefficient[1/Sqrt[1-4*x-36*x^2],{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 15 2012 *)
%o A098455 (PARI) x='x+O('x^66); Vec(1/sqrt(1-4*x-36*x^2)) \\ _Joerg Arndt_, May 11 2013
%Y A098455 Cf. A387428.
%K A098455 easy,nonn,changed
%O A098455 0,2
%A A098455 _Paul Barry_, Sep 08 2004