A381670 - OEIS

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)).

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

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OFFSET

0,3

COMMENTS

Conjecture: All terms are powers of two.

LINKS

Table of n, a(n) for n=0..30.

PROG

(PARI)

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<max_n, v=optimize(v); out=concat(out, denominator(v[#v]))); out }