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 A098341 #41 Dec 04 2021 12:35:19
%S A098341 1,3,1,-45,-255,-477,2689,25203,82945,-90045,-2379519,-11581677,
%T A098341 -12063999,197669475,1423716225,3645266355,-12180238335,-156702949245,
%U A098341 -626511576575,51239061075,15179398450945,87687927568035,151934475887745
%N A098341 Expansion of 1/sqrt(1 - 6*x + 25*x^2).
%C A098341 Central coefficients of (1 + 3*x - 4*x^2)^n.
%C A098341 (-1)^n*a(n) is the sum of squares of coefficients of (1+2*i*x)^n where i=sqrt(-1) (see PARI code). - _Joerg Arndt_, Jul 06 2011
%C A098341 Binomial transform of A098337.
%C A098341 Second binomial transform of A098334.
%H A098341 Seiichi Manyama, <a href="/A098341/b098341.txt">Table of n, a(n) for n = 0..1000</a>
%H A098341 Hacène Belbachir and Abdelghani Mehdaoui, <a href="https://doi.org/10.2989/16073606.2020.1729269">Recurrence relation associated with the sums of square binomial coefficients</a>, Quaestiones Mathematicae (2021) Vol. 44, Issue 5, 615-624.
%H A098341 Hacène Belbachir, Abdelghani Mehdaoui, and 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 A098341 Tony D. Noe, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Noe/noe35.html">On the Divisibility of Generalized Central Trinomial Coefficients</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A098341 E.g.f.: exp(3*x)*BesselI(0, 4*I*x), I=sqrt(-1).
%F A098341 a(n) = (-1)^n*Sum_{k=0..n} binomial(n, k)^2*(-4)^k.
%F A098341 a(n) = (-1)^n*hypergeometric([-n,-n], [1], -4). - _Peter Luschny_, Sep 23 2014
%F A098341 D-finite with recurrence: n*a(n) +3*(-2*n+1)*a(n-1) +25*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 27 2014
%F A098341 From _Peter Bala_, Nov 28 2021: (Start)
%F A098341 a(n) = (5^n)*P(n,3/5), where P(n,x) is the n-th Legendre polynomial.
%F A098341 a(n) = [x^n] ((1 - x)*(1 + 4*x))^n.
%F A098341 a(n) = 5^(2*n+1)*Sum_{k >= n} (-1)^(n+k)*binomial(k,n)^2*(1/4)^(k+1).
%F A098341 a(n) = (5/4)*(25/4)^n*hypergeom([n+1, n+1], [1], -1/4). (End)
%t A098341 Table[(-5)^n*LegendreP[n,-3/5],{n,0,20}] (* _Vaclav Kotesovec_, Jul 23 2013 *)
%t A098341 CoefficientList[Series[1/Sqrt[1-6x+25x^2],{x,0,30}],x] (* _Harvey P. Dale_, Aug 22 2014 *)
%o A098341 (PARI) a(n)={local(v=Vec((1+2*I*x)^n)); (-1)^n*sum(k=1,#v,v[k]^2);} /* Joerg Arndt, Jul 06 2011 */
%o A098341 (PARI) a(n)={local(v=Vec((1+2*I*x)^n)); sum(k=1,#v, real(v[k])^2-imag(v[k])^2);} /* Joerg Arndt, Jul 06 2011 */
%o A098341 (Sage)
%o A098341 A098341 = lambda n: (-1)^n*hypergeometric([-n,-n], [1], -4)
%o A098341 [Integer(A098341(n).n(100)) for n in (0..22)] # _Peter Luschny_, Sep 23 2014
%Y A098341 Cf. A098332, A012000, A116091, A126869.
%K A098341 easy,sign
%O A098341 0,2
%A A098341 _Paul Barry_, Sep 03 2004