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 A371341 #14 Apr 22 2024 13:12:40
%S A371341 1,2,6,46,330,2778,24094,219318,2048274,19583410,190497142,1880184446,
%T A371341 18778814938,189456108554,1927852050830,19763367194630,
%U A371341 203919590002210,2116079501498722,22069907395614182,231222485352688590,2432325883912444010
%N A371341 G.f. A(x) satisfies A(x) = 1 + x/A(x) * (1 + A(x)^5).
%F A371341 a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n-5*k-2,n-1) for n > 0.
%p A371341 A371341 := proc(n)
%p A371341 if n = 0 then
%p A371341 1;
%p A371341 else
%p A371341 add(binomial(n,k)*binomial(2*n-5*k-2,n-1),k=0..n) ;
%p A371341 (-1)^(n-1)*%/n ;
%p A371341 end if;
%p A371341 end proc:
%p A371341 seq(A371341(n),n=0..60) ; # _R. J. Mathar_, Apr 22 2024
%o A371341 (PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n-5*k-2, n-1))/n);
%Y A371341 Cf. A112478, A348957, A364394, A364395, A366363, A371892.
%K A371341 nonn
%O A371341 0,2
%A A371341 _Seiichi Manyama_, Apr 12 2024