Search: id:A143136
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%I A143136
%S A143136 1,2,12,128,1920,36992,870912,24232448,777999360,28309164032,
%T A143136 1151292628992,51750540443648,2547747292446720,136336755956252672,
%U A143136 7879446478581399552,489119124160488931328,32456290094449950720000
%N A143136 E.g.f. satisfies: A(x) = x + sinh( A(x) )^2.
%C A143136 Radius of convergence is r = log(sqrt(2)+1)/2 - (sqrt(2)-1)/2 = 0.2335800...,
%C A143136 where A(r) = log(1+sqrt(2))/2 = asinh(1)/2 = 0.44068679...
%F A143136 E.g.f.: A(x) = Series_Reversion( x - sinh(x)^2 ).
%F A143136 E.g.f. derivative: A'(x) = 1/(1 - sinh(2*A(x))).
%e A143136 A(x) = x + 2*x^2/2! + 12*x^3/3! + 128*x^4/4! + 1920*x^5/5! +...
%e A143136 sinh(A(x)) = G(x) is the e.g.f. of A143137:
%e A143136 G(x) = x + 2*x^2/2! + 13*x^3/3! + 140*x^4/4! + 2101*x^5/5! +...
%o A143136 (PARI) {a(n)=n!*polcoeff(serreverse(x-sinh(x+x*O(x^n))^2),n)}
%o A143136 (PARI) {a(n)=local(A=x);for(i=0,n,A=x + sinh(A)^2);n!*polcoeff(A,n)}
%Y A143136 Cf. A143134, A143137.
%Y A143136 Sequence in context: A039933 A035351 A003712 this_sequence A097629 A014235 
               A098628
%Y A143136 Adjacent sequences: A143133 A143134 A143135 this_sequence A143137 A143138 
               A143139
%K A143136 nonn
%O A143136 1,2
%A A143136 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 27 2008

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