|
%I #12 Jul 25 2023 07:32:47
%S 1,1,-6,-21,286,1281,-20592,-100226,1749462,8899086,-162993402,
%T -852079872,16106878320,85783258295,-1658113447608,-8950840125828,
%U 175904428301062,959332126312266,-19096256882857668,-104984591307499239,2111233112316364434
%N G.f. satisfies A(x) = 1 + x*A(-x)^6.
%H Seiichi Manyama, <a href="/A143049/b143049.txt">Table of n, a(n) for n = 0..500</a>
%F G.f. satisfies: A(x) = 1 + x*(1 - x*A(x)^6)^6.
%F G.f. satisfies: [A(x)^7 + A(-x)^7]/2 = [A(x)^6 + A(-x)^6]/2.
%e A(x) = 1 + x - 6*x^2 - 21*x^3 + 286*x^4 + 1281*x^5 - 20592*x^6 -++-...
%e A(x)^6 = 1 + 6*x - 21*x^2 - 286*x^3 + 1281*x^4 + 20592*x^5 - 100226*x^6 -...
%e A(x)^7 = 1 + 7*x - 21*x^2 - 364*x^3 + 1281*x^4 + 27027*x^5 - 100226*x^6 -...
%e Note that a bisection of A^7 equals a bisection of A^6.
%o (PARI) a(n)=local(A=x+x*O(x^n));for(i=0,n,A=1+x*subst(A,x,-x)^6);polcoeff(A,n)
%Y Cf. A143045, A143046, A143047, A143048, A213252, A213281, A213335.
%Y Cf. A171206.
%K sign
%O 0,3
%A _Paul D. Hanna_, Jul 19 2008
|
