A277033 G.f. A(x) satisfies: A(x - A(-x)^2) = x + A(x)^2.

1, 2, 4, 18, 76, 420, 2248, 14410, 89676, 642764, 4487896, 35282228, 271094936, 2310824808, 19309255952, 177093587874, 1596354765308, 15664040851996, 151403517122328, 1582290415072396, 16319413287176584, 180949924453071544, 1983128441367699632, 23249895784026465044, 269763155110100504568, 3333619355332522429656

Offset: 1

Author

Paul D. Hanna, Oct 09 2016

Keywords

• nonn

Examples

			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 -...
		

Crossrefs

Cf. A277034, A275765.

Programs

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),", "))

Formula

G.f. A(x) satisfies: A(-A(-x)) = x.