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 A116092 #24 Jul 23 2025 22:47:31
%S A116092 1,-4,-8,224,-1184,-2944,84736,-467968,-1235456,35956736,-202108928,
%T A116092 -548651008,16063381504,-91151859712,-251452325888,7389369073664,
%U A116092 -42180470767616,-117581870006272,3464100777558016,-19854347412176896,-55753417460547584,1645577388148391936
%N A116092 Expansion of 1/sqrt(1+8*x+64*x^2).
%C A116092 8th binomial transform is expansion of 1/sqrt(1-8*x+64*x^2).
%H A116092 G. C. Greubel, <a href="/A116092/b116092.txt">Table of n, a(n) for n = 0..1000</a>
%H A116092 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 A116092 E.g.f.: exp(-4*x)*Bessel_I(0, 2*sqrt(-12)*x).
%F A116092 a(n) = 2^n*Sum_{k=0..n} C(n,n-k)*C(n,k)*(-3)^k.
%F A116092 a(n) = 2^n*A116091(n).
%F A116092 D-finite with recurrence: n*a(n) +4*(2*n-1)*a(n-1) +64*(n-1)*a(n-2)=0. - _R. J. Mathar_, Nov 07 2012
%t A116092 CoefficientList[Series[1/Sqrt[1+8*x+64*x^2], {x, 0, 30}], x] (* _G. C. Greubel_, May 10 2019 *)
%o A116092 (PARI) my(x='x+O('x^30)); Vec(1/sqrt(1+8*x+64*x^2)) \\ _G. C. Greubel_, May 10 2019
%o A116092 (Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( 1/Sqrt(1+8*x+64*x^2) )); // _G. C. Greubel_, May 10 2019
%o A116092 (Sage) (1/sqrt(1+8*x+64*x^2)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, May 10 2019
%o A116092 (GAP) List([0..30], n-> 2^n*Sum([0..n], k-> (-3)^k*Binomial(n,k)* Binomial(n, n-k))); # _G. C. Greubel_, May 10 2019
%Y A116092 Cf. A116091.
%K A116092 easy,sign
%O A116092 0,2
%A A116092 _Paul Barry_, Feb 04 2006