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 A143551 #6 Jul 08 2025 07:41:54
%S A143551 1,1,4,29,196,1781,14000,139234,1176340,12283166,108258380,1165438808,
%T A143551 10561185568,116096795195,1072964739264,11975785105572,
%U A143551 112313638368948,1268177365551626,12029082865935512,137067430786661911
%N A143551 G.f. A(x) satisfies A(x) = 1 + x*A(x)^5*A(-x).
%F A143551 G.f. satisfies: A(x) + A(-x) = 1 + [A(x)*A(-x)] + x^2*[A(x)*A(-x)]^6.
%F A143551 a(0) = 1; a(n) = Sum_{x_1, x_2, ..., x_6>=0 and x_1+x_2+...+x_6=n-1} (-1)^x_1 * Product_{k=1..6} a(x_k). - _Seiichi Manyama_, Jul 08 2025
%e A143551 G.f. A(x) = 1 + x + 4*x^2 + 29*x^3 + 196*x^4 + 1781*x^5 + 14000*x^6 +...
%e A143551 Related expansions:
%e A143551 A(x)^5 = 1 + 5*x + 30*x^2 + 235*x^3 + 1845*x^4 + 16576*x^5 + 144270*x^6 +...
%e A143551 A(x)*A(-x) = 1 + 7*x^2 + 350*x^4 + 25165*x^6 + 2121330*x^8 +...
%e A143551 [A(x)*A(-x)]^6 = 1 + 42*x^2 + 2835*x^4 + 231350*x^6 +...
%o A143551 (PARI) {a(n)=local(A=1+x*O(x^n));for(i=0,n,A=1+x*A^5*subst(A,x,-x));polcoeff(A,n)}
%Y A143551 Cf. A143550, A143552, A143553, A143554.
%K A143551 nonn
%O A143551 0,3
%A A143551 _Paul D. Hanna_, Aug 24 2008