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)).

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

0,9

Links

Table of n, a(n) for n=0..27.

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=[0, 1]); while(#v<max_n, v=optimize(v); out=concat(out, numerator(v[#v]))); out }

Crossrefs

Cf. A381670 ( denominators ).

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)) ).

Sequence in context: A159432 A151645 A115486 * A157885 A204377 A242557

Adjacent sequences: A381666 A381667 A381668 * A381670 A381671 A381672

Keyword

sign,frac,eigen

Author

Thomas Scheuerle, Mar 03 2025

Status

approved