A381669
The function A(x) = x+(1/2)*x^2-(1/16)*x^4... = Sum_{k >= 0} x^k*a(k)/A381670(k) satisfies the functional equation: x*(A(x)+1) = A(A(x)).
Original entry on oeis.org
0, 1, 1, 0, -1, 1, -1, -1, 113, -19, -1049, 849, 10171, -67975, 183735, 143679, -81627111, -135422127, 3045667427, 341639611, -225862086367, 212228801943, 8911194501081, -5123304557653, -1496818714531027, 6387545555294289, 64005829810291411, -250179519280324047
Offset: 0
Cf.
A381666 ( A(x)+x = x*A(A(x)) ).
Cf.
A030266 ( A(x)-x = x*A(A(x)) ).
Cf.
A347080 ( A(x)-x = x*A(A(-x)) ).
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compose(v) = polcoeff(subst(Polrev(v),x,Polrev(v)),#v-1)
optimize(v) = { my(r=1,z = v[#v],t = compose(concat(v,r))); while(t<>z, r = r+(z-t)/2; t = compose(concat(v,r)));concat(v,r) }
listA(max_n) = { my(v=[0, 1], out=[0, 1]); while(#v
A381666
The generating function A(x) satisfies the functional equation: A(x)+x = x*A(A(x)).
Original entry on oeis.org
0, -1, 1, 0, -2, 1, 10, -13, -70, 163, 585, -2162, -5361, 30588, 49870, -459125, -411370, 7257651, 1513653, -119997558, 56857538, 2062729507, -2444340720, -36662245639, 71849171621, 670108236318, -1904023701457, -12520858710212, 48731008916451, 237412587011506, -1237341547854760
Offset: 0
G.f.: A(x) = -x + x^2 - 2*x^4 + x^5 + 10*x^6 + ...
A(A(x)) = x - 2*x^3 + x^4 + 10*x^5 - 13*x^6 + ...
Cf.
A030266 ( A(x)-x = x*A(A(x)) ).
Cf.
A347080 ( A(x)-x = x*A(A(-x)) ).
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a(n) = { my(A=-1+x); for(i=0, n, A=-1+x*A*subst(A, x, x*A+x*O(x^n))); if(n==0,0,polcoeff(A, n-1))}
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