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)) ).
-
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
A381670
The function A(x) = x+(1/2)*x^2-(1/16)*x^4... = Sum_{k >= 0} x^k*A381669(k)/a(k) satisfies the functional equation: x*(A(x)+1) = A(A(x)).
Original entry on oeis.org
1, 1, 2, 1, 16, 16, 64, 16, 1024, 1024, 4096, 2048, 32768, 32768, 131072, 16384, 4194304, 4194304, 16777216, 8388608, 134217728, 134217728, 536870912, 134217728, 8589934592, 8589934592, 34359738368, 17179869184, 274877906944, 274877906944, 1099511627776
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)) ).
-
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=[1,1]); while(#v
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