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Search: id:A143136
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| A143136 |
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E.g.f. satisfies: A(x) = x + sinh( A(x) )^2. |
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+0
3
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| 1, 2, 12, 128, 1920, 36992, 870912, 24232448, 777999360, 28309164032, 1151292628992, 51750540443648, 2547747292446720, 136336755956252672, 7879446478581399552, 489119124160488931328, 32456290094449950720000
(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 is r = log(sqrt(2)+1)/2 - (sqrt(2)-1)/2 = 0.2335800...,
where A(r) = log(1+sqrt(2))/2 = asinh(1)/2 = 0.44068679...
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FORMULA
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E.g.f.: A(x) = Series_Reversion( x - sinh(x)^2 ).
E.g.f. derivative: A'(x) = 1/(1 - sinh(2*A(x))).
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EXAMPLE
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A(x) = x + 2*x^2/2! + 12*x^3/3! + 128*x^4/4! + 1920*x^5/5! +...
sinh(A(x)) = G(x) is the e.g.f. of A143137:
G(x) = x + 2*x^2/2! + 13*x^3/3! + 140*x^4/4! + 2101*x^5/5! +...
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PROGRAM
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(PARI) {a(n)=n!*polcoeff(serreverse(x-sinh(x+x*O(x^n))^2), n)}
(PARI) {a(n)=local(A=x); for(i=0, n, A=x + sinh(A)^2); n!*polcoeff(A, n)}
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CROSSREFS
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Cf. A143134, A143137.
Sequence in context: A039933 A035351 A003712 this_sequence A097629 A014235 A098628
Adjacent sequences: A143133 A143134 A143135 this_sequence A143137 A143138 A143139
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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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