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Search: id:A143134
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| A143134 |
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E.g.f. satisfies: A(x) = x + sin( A(x) )^2 with A(0)=0. |
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3
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| 1, 2, 12, 112, 1440, 23552, 467712, 10926592, 293544960, 8914583552, 301957742592, 11285975498752, 461367611228160, 20477098870833152, 980591931131953152, 50393637174029320192, 2766350676943951626240
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Radius of convergence of A(x) is r = Pi/4 - 1/2, with A(r) = Pi/4.
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FORMULA
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E.g.f.: A(x) = Series_Reversion( x - sin(x)^2 ).
E.g.f. derivative: A'(x) = 1/(1 - 2*sqrt(A(x)-x)*sqrt(1+x-A(x))); thus A'(x) = 1/(1 - sin(2*A(x))).
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EXAMPLE
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A(x) = x + 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
sin(A(x)) = G(x) is the e.g.f. of A143135:
G(x) = x + 2*x^2/2! + 11*x^3/3! + 100*x^4/4! + 1261*x^5/5! +...
G(x)^2 = 2*x^2/2! + 12*x^3/3! + 112*x^4/4! + 1440*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=local(A=x); for(i=0, n, A=x + sin(A)^2); n!*polcoeff(A, n)}
(PARI) {a(n)=n!*polcoeff(serreverse(x-sin(x+x*O(x^n))^2), n)}
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CROSSREFS
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Cf. A143135, A143136.
Sequence in context: A047855 A009232 A124213 this_sequence A091481 A053312 A091854
Adjacent sequences: A143131 A143132 A143133 this_sequence A143135 A143136 A143137
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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 27 2008
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