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 A376792 #13 Apr 30 2025 09:11:45
%S A376792 1,2,6,20,71,258,954,3572,13501,51404,196858,757472,2926097,11341032,
%T A376792 44080770,171755976,670664951,2623732322,10281616176,40350944112,
%U A376792 158573538071,623930435834,2457658576132,9690467310480,38244489565051,151064227161784,597165099484632
%N A376792 Expansion of 1/sqrt((1 - x^4)^2 - 4*x).
%C A376792 From _Seiichi Manyama_, Apr 30 2025: (Start)
%C A376792 Number of lattice paths from (0,0) to (n,n) using steps (1,0),(0,1),(4,4).
%C A376792 Diagonal of the rational function 1 / (1 - x - y - x^4*y^4). (End)
%F A376792 a(n) = Sum_{k=0..floor(n/4)} binomial(2*n-7*k,k) * binomial(2*n-8*k,n-4*k).
%o A376792 (PARI) my(N=30, x='x+O('x^N)); Vec(1/sqrt((1-x^4)^2-4*x))
%o A376792 (PARI) a(n) = sum(k=0, n\4, binomial(2*n-7*k, k)*binomial(2*n-8*k, n-4*k));
%Y A376792 Cf. A001850, A349713, A376791.
%Y A376792 Cf. A098482.
%K A376792 nonn
%O A376792 0,2
%A A376792 _Seiichi Manyama_, Oct 04 2024