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Search: id:A141366
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| A141366 |
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G.f.: A(x) = x - A(-A(x)^2). |
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+0
1
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| 1, 1, 2, 4, 8, 16, 32, 65, 138, 316, 792, 2142, 6052, 17316, 49160, 137108, 374632, 1004668, 2656872, 6974510, 18310220, 48416528, 129637152, 352339898, 971336204, 2707410220, 7596357720, 21363062480, 60019857952, 168132717792
(list; graph; listen)
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OFFSET
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1,3
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FORMULA
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G.f.: A(x) = Series_Reversion( x + A(-x^2) ).
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EXAMPLE
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G.f.: A(x) = x + x^2 + 2*x^3 + 4*x^4 + 8*x^5 + 16*x^6 + 32*x^7 + 65*x^8 +...
A(x)^2 = x^2 + 2*x^3 + 5*x^4 + 12*x^5 + 28*x^6 + 64*x^7 + 144*x^8 +...
Series_Reversion( A(x) ) = x + A(-x^2), thus:
x = A(x - x^2 + x^4 - 2*x^6 + 4*x^8 - 8*x^10 + 16*x^12 -+...).
What is Limit a(n+1)/a(n) = ? ; a(501)/a(500) = 2.91525180...
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PROGRAM
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(PARI) {a(n)=local(A=x+x^2); for(i=0, n, A=x-subst(A, x, -(A+x*O(x^n))^2)); polcoeff(A, n)}
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CROSSREFS
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Sequence in context: A098051 A084637 A100137 this_sequence A049142 A100138 A100139
Adjacent sequences: A141363 A141364 A141365 this_sequence A141367 A141368 A141369
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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), Jul 18 2008
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