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 A374598 #13 Jul 13 2024 13:48:11
%S A374598 1,2,6,24,94,372,1508,6192,25638,106908,448356,1889040,7989676,
%T A374598 33902504,144259944,615330784,2630199942,11263613484,48315367076,
%U A374598 207556060816,892819376964,3845161246424,16578320962104,71548426931616,309070048163676,1336223562436632
%N A374598 Expansion of 1/sqrt(1 - 4*x - 8*x^3).
%H A374598 Seiichi Manyama, <a href="/A374598/b374598.txt">Table of n, a(n) for n = 0..1000</a>
%F A374598 a(n) = Sum_{k=0..floor(n/3)} 2^k * binomial(n-2*k,k) * binomial(2*(n-2*k),n-2*k).
%F A374598 n*a(n) = 2*(2*n-1)*a(n-1) + 4*(2*n-3)*a(n-3).
%o A374598 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt(1-4*x-8*x^3))
%o A374598 (PARI) a(n) = sum(k=0, n\3, 2^k*binomial(n-2*k, k)*binomial(2*(n-2*k), n-2*k));
%Y A374598 Cf. A157004, A360266.
%Y A374598 Cf. A084609, A374599.
%K A374598 nonn
%O A374598 0,2
%A A374598 _Seiichi Manyama_, Jul 13 2024