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A277034
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G.f. A(x) satisfies: A(x - A(x)^2) = x + A(-x)^2.
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1
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1, 2, 4, 50, 268, 3780, 28872, 438410, 4087180, 65365260, 697738072, 11624944660, 137432369816, 2371412517480, 30441246407440, 542177876315970, 7460629909188796, 136882304192481020, 2001263659780301080, 37777108180867675020, 583057080531893501960, 11314432259935102732856, 183452721005994056356272
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f. A(x) satisfies: A(-A(-x)) = x.
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EXAMPLE
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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 +...
such that A(x - A(x)^2) = x + A(-x)^2.
RELATED SERIES.
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 +...
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 +...
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 -...
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PROG
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(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)}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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