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 A383572 #9 Apr 30 2025 09:11:32
%S A383572 1,0,0,0,1,2,0,0,1,6,6,0,1,12,30,20,1,20,90,140,71,30,210,560,631,294,
%T A383572 420,1680,3151,2828,1680,4200,11551,16704,13272,12672,34651,72162,
%U A383572 86064,69960,102961,252362,423390,446160,429001,805508,1685970,2393820,2419561
%N A383572 Expansion of 1/sqrt((1-x^4)^2 - 4*x^5).
%C A383572 Number of lattice paths from (0,0) to (n,n) using steps (5,0),(0,5),(4,4).
%C A383572 Diagonal of the rational function 1 / (1 - x^5 - y^5 - x^4*y^4).
%F A383572 a(n) = Sum_{k=0..floor(n/4)} binomial(n-3*k,k) * binomial(k,n-4*k).
%o A383572 (PARI) a(n) = sum(k=0, n\4, binomial(n-3*k, k)*binomial(k, n-4*k));
%Y A383572 Cf. A002426, A182883, A383571.
%Y A383572 Cf. A376792.
%K A383572 nonn
%O A383572 0,6
%A A383572 _Seiichi Manyama_, Apr 30 2025