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 A343842 #22 Jul 25 2024 08:46:38
%S A343842 1,-4,24,-160,1120,-8064,59136,-439296,3294720,-24893440,189190144,
%T A343842 -1444724736,11076222976,-85201715200,657270374400,-5082890895360,
%U A343842 39392404439040,-305870434467840,2378992268083200,-18531097667174400,144542561803960320,-1128808577897594880
%N A343842 Series expansion of 1/sqrt(8*x^2 + 1), even powers only.
%C A343842 Essentially the inverse binomial convolution of the Delannoy numbers.
%F A343842 a(n) = n! * [x^n] BesselJ(0, sqrt(8)*x).
%F A343842 D-finite with recurrence a(n) = 4*(1 - 2*n)*a(n - 1) / n for n >= 2.
%F A343842 a(n) = A(2*n) where A(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n, k)*A008288(n, k).
%p A343842 gf := 1/sqrt(8*x^2 + 1): ser := series(gf, x, 32):
%p A343842 seq(coeff(ser, x, 2*n), n = 0..21);
%t A343842 Take[CoefficientList[Series[1/Sqrt[8*x^2 + 1], {x, 0, 42}], x], {1, -1, 2}] (* _Amiram Eldar_, May 05 2021 *)
%o A343842 (PARI) my(x='x+O('x^25)); Vec(1/sqrt(8*x + 1)) \\ _Michel Marcus_, May 04 2021
%Y A343842 Signed version of A059304.
%Y A343842 Cf. A008288, A006139.
%K A343842 sign,easy
%O A343842 0,2
%A A343842 _Peter Luschny_, May 04 2021