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Search: id:A145348
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| A145348 |
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G.f. satisfies: A(x/A(x)^2) = 1 + x*A(x)^2. |
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+0
3
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| 1, 1, 4, 30, 312, 3965, 57824, 933998, 16346728, 305539046, 6037780164, 125227212342, 2711254371568, 61021656441091, 1423063422363676, 34297379607790288, 852463916004336464, 21812807282389353798
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: A(x) = 1 + x*G(x)^4 where G(x) = A(x*G(x)^2) and A(x) = G(x/A(x)^2).
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EXAMPLE
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G.f.: A(x) = 1 + x + 4*x^2 + 30*x^3 + 312*x^4 + 3965*x^5 +...
A(x)^2 = 1 + 2*x + 9*x^2 + 68*x^3 + 700*x^4 + 8794*x^5 + 126974*x^6+..
A(x/A(x)^2) = 1 + x + 2*x^2 + 9*x^3 + 68*x^4 + 700*x^5 + 8794*x^6 +...
A(x) = 1 + x*G(x)^4 where G(x) = A(x*G(x)^2):
G(x) = 1 + x + 6*x^2 + 59*x^3 + 742*x^4 + 10877*x^5 + 177612*x^6 +...
G(x)^2 = 1 + 2*x + 13*x^2 + 130*x^3 + 1638*x^4 + 23946*x^5 +...
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PROGRAM
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(PARI) {a(n)=local(F=1+x, G); for(i=0, n, G=serreverse(x/(F+x*O(x^n))^2)/x; F=1+x*G^2); polcoeff(F, n)}
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CROSSREFS
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Adjacent sequences: A145345 A145346 A145347 this_sequence A145349 A145350 A145351
Sequence in context: A054972 A052452 A088794 this_sequence A052574 A158834 A139086
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 09 2008
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