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 A277034 G.f. A(x) satisfies: A(x - A(x)^2) = x + A(-x)^2. 1

%I #5 Oct 09 2016 19:45:46

%S 1,2,4,50,268,3780,28872,438410,4087180,65365260,697738072,

%T 11624944660,137432369816,2371412517480,30441246407440,

%U 542177876315970,7460629909188796,136882304192481020,2001263659780301080,37777108180867675020,583057080531893501960,11314432259935102732856,183452721005994056356272

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

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

%e G.f.: A(x) = x + 2*x^2 + 4*x^3 + 50*x^4 + 268*x^5 + 3780*x^6 + 28872*x^7 + 438410*x^8 + 4087180*x^9 + 65365260*x^10 +...

%e such that A(x - A(x)^2) = x + A(-x)^2.

%e RELATED SERIES.

%e A(x)^2 = x^2 + 4*x^3 + 12*x^4 + 116*x^5 + 752*x^6 + 9032*x^7 + 77508*x^8 + 1049348*x^9 + 10608800*x^10 + 155499800*x^11 + 1763239416*x^12 +...

%e sqrt((A(x) - x)/2) = x + x^2 + 12*x^3 + 55*x^4 + 818*x^5 + 5740*x^6 + 92534*x^7 + 815391*x^8 + 13765254*x^9 + 141099882*x^10 + 2462940118*x^11 +...

%e Series_Reversion( sqrt((A(x) - x)/2) ) = x - x^2 - 10*x^3 - 294*x^5 - 24998*x^7 - 3158794*x^9 - 506665836*x^11 - 96305392110*x^13 - 20904881285306*x^15 - 5068120123901550*x^17 - 1352637633479800560*x^19 - 393510296576306819932*x^21 -...

%o (PARI) {a(n) = my(A=x,R); for(i=1,n, R = subst(A,x,-x + x*O(x^n)); A = subst(x + R^2, x, serreverse(x - A^2 + x*O(x^n)))); polcoeff(A,n)}

%o for(n=1,30,print1(a(n),", "))

%Y Cf. A277033, A275765.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Oct 09 2016

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Last modified December 5 23:11 EST 2023. Contains 367594 sequences. (Running on oeis4.)