OFFSET
1,2
FORMULA
G.f. A(x) satisfies: A(-A(-x)) = x.
EXAMPLE
G.f.: A(x) = x + 2*x^2 + 4*x^3 + 18*x^4 + 76*x^5 + 420*x^6 + 2248*x^7 + 14410*x^8 + 89676*x^9 + 642764*x^10 +...
such that A(x - A(-x)^2) = x + A(x)^2.
RELATED SERIES.
A(x)^2 = x^2 + 4*x^3 + 12*x^4 + 52*x^5 + 240*x^6 + 1288*x^7 + 7108*x^8 + 43908*x^9 + 275872*x^10 + 1904280*x^11 + 13301112*x^12 +...
sqrt((A(x) - x)/2) = x + x^2 + 4*x^3 + 15*x^4 + 82*x^5 + 420*x^6 + 2742*x^7 + 16767*x^8 + 123294*x^9 + 856042*x^10 + 6906790*x^11 + 53066832*x^12 +...
Series_Reversion( sqrt((A(x) - x)/2) ) = x - x^2 - 2*x^3 - 14*x^5 - 406*x^7 - 16514*x^9 - 872812*x^11 - 56605438*x^13 - 4346269882*x^15 - 386603411414*x^17 - 39262351744912*x^19 - 4504838187841052*x^21 -...
PROG
(PARI) {a(n) = my(A=x, R); for(i=1, n, R = subst(A, x, -x + x*O(x^n)); A = subst(x + A^2, x, serreverse(x - R^2))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 09 2016
STATUS
approved